diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt
index b25db6e0f..50e44e81c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt
@@ -162,7 +162,7 @@ public interface Strides {
     /**
      * Array strides
      */
-    public val strides: List<Int>
+    public val strides: IntArray
 
     /**
      * Get linear index from multidimensional index
@@ -189,6 +189,11 @@ public interface Strides {
     }
 }
 
+internal inline fun offsetFromIndex(index: IntArray, shape: IntArray, strides: IntArray): Int = index.mapIndexed { i, value ->
+    if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${shape[i]})")
+    value * strides[i]
+}.sum()
+
 /**
  * Simple implementation of [Strides].
  */
@@ -199,7 +204,7 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
     /**
      * Strides for memory access
      */
-    override val strides: List<Int> by lazy {
+    override val strides: IntArray by lazy {
         sequence {
             var current = 1
             yield(1)
@@ -208,13 +213,10 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
                 current *= it
                 yield(current)
             }
-        }.toList()
+        }.toList().toIntArray()
     }
 
-    override fun offset(index: IntArray): Int = index.mapIndexed { i, value ->
-        if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
-        value * strides[i]
-    }.sum()
+    override fun offset(index: IntArray): Int = offsetFromIndex(index, shape, strides)
 
     override fun index(offset: Int): IntArray {
         val res = IntArray(shape.size)
@@ -323,8 +325,7 @@ public inline fun <T, reified R : Any> NDStructure<T>.mapToBuffer(
 /**
  * Mutable ND buffer based on linear [MutableBuffer].
  */
-
-public class MutableNDBuffer<T>(
+public open class MutableNDBuffer<T>(
     strides: Strides,
     buffer: MutableBuffer<T>,
 ) : NDBuffer<T>(strides, buffer), MutableNDStructure<T> {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
new file mode 100644
index 000000000..0a28ace4f
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
@@ -0,0 +1,173 @@
+package space.kscience.kmath.tensors
+
+import space.kscience.kmath.nd.MutableNDBuffer
+import space.kscience.kmath.structures.RealBuffer
+import space.kscience.kmath.structures.array
+
+
+public class RealTensor(
+    override val shape: IntArray,
+    buffer: DoubleArray
+) :
+    TensorStructure<Double>,
+    MutableNDBuffer<Double>(
+        TensorStrides(shape),
+        RealBuffer(buffer)
+    ) {
+    override fun item(): Double = buffer[0]
+}
+
+public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor> {
+
+    override fun add(a: RealTensor, b: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun multiply(a: RealTensor, k: Number): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override val zero: RealTensor
+        get() = TODO("Not yet implemented")
+
+    override fun multiply(a: RealTensor, b: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override val one: RealTensor
+        get() = TODO("Not yet implemented")
+
+
+    override fun Double.plus(other: RealTensor): RealTensor {
+        val n = other.buffer.size
+        val arr = other.buffer.array
+        val res = DoubleArray(n)
+        for (i in 1..n)
+            res[i - 1] = arr[i - 1] + this
+        return RealTensor(other.shape, res)
+    }
+
+    override fun RealTensor.plus(value: Double): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.plusAssign(value: Double) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.plusAssign(other: RealTensor) {
+        TODO("Not yet implemented")
+    }
+
+    override fun Double.minus(other: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.minus(value: Double): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.minusAssign(value: Double) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.minusAssign(other: RealTensor) {
+        TODO("Not yet implemented")
+    }
+
+    override fun Double.times(other: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.times(value: Double): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.timesAssign(value: Double) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.timesAssign(other: RealTensor) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.dot(other: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.dotAssign(other: RealTensor) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.dotRightAssign(other: RealTensor) {
+        TODO("Not yet implemented")
+    }
+
+    override fun diagonalEmbedding(diagonalEntries: RealTensor, offset: Int, dim1: Int, dim2: Int): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.transpose(i: Int, j: Int): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.transposeAssign(i: Int, j: Int) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.view(shape: IntArray): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.abs(): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.absAssign() {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.sum(): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.sumAssign() {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.div(other: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.divAssign(other: RealTensor) {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.exp(): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.expAssign() {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.log(): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.logAssign() {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.svd(): Triple<RealTensor, RealTensor, RealTensor> {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.symEig(eigenvectors: Boolean): Pair<RealTensor, RealTensor> {
+        TODO("Not yet implemented")
+    }
+
+}
+
+public inline fun <R> RealTensorAlgebra(block: RealTensorAlgebra.() -> R): R =
+    RealTensorAlgebra().block()
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt
index cf16769c9..83c45feec 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt
@@ -1,70 +1,114 @@
 package space.kscience.kmath.tensors
 
-import space.kscience.kmath.nd.MutableNDStructure
-
-public interface TensorStructure<T> : MutableNDStructure<T> {
-    // A tensor can have empty shape, in which case it represents just a value
-    public fun value(): T
-}
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.RingWithNumbers
 
 // https://proofwiki.org/wiki/Definition:Algebra_over_Ring
-
-public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
+public interface TensorAlgebra<T, TensorType : TensorStructure<T>>: RingWithNumbers<TensorType> {
 
     public operator fun T.plus(other: TensorType): TensorType
     public operator fun TensorType.plus(value: T): TensorType
-    public operator fun TensorType.plus(other: TensorType): TensorType
     public operator fun TensorType.plusAssign(value: T): Unit
     public operator fun TensorType.plusAssign(other: TensorType): Unit
 
     public operator fun T.minus(other: TensorType): TensorType
     public operator fun TensorType.minus(value: T): TensorType
-    public operator fun TensorType.minus(other: TensorType): TensorType
     public operator fun TensorType.minusAssign(value: T): Unit
     public operator fun TensorType.minusAssign(other: TensorType): Unit
 
     public operator fun T.times(other: TensorType): TensorType
     public operator fun TensorType.times(value: T): TensorType
-    public operator fun TensorType.times(other: TensorType): TensorType
     public operator fun TensorType.timesAssign(value: T): Unit
     public operator fun TensorType.timesAssign(other: TensorType): Unit
-    public operator fun TensorType.unaryMinus(): TensorType
 
 
+    //https://pytorch.org/docs/stable/generated/torch.matmul.html
     public infix fun TensorType.dot(other: TensorType): TensorType
     public infix fun TensorType.dotAssign(other: TensorType): Unit
     public infix fun TensorType.dotRightAssign(other: TensorType): Unit
 
+    //https://pytorch.org/docs/stable/generated/torch.diag_embed.html
     public fun diagonalEmbedding(
         diagonalEntries: TensorType,
         offset: Int = 0, dim1: Int = -2, dim2: Int = -1
     ): TensorType
 
+    //https://pytorch.org/docs/stable/generated/torch.transpose.html
     public fun TensorType.transpose(i: Int, j: Int): TensorType
     public fun TensorType.transposeAssign(i: Int, j: Int): Unit
 
+    //https://pytorch.org/docs/stable/tensor_view.html
     public fun TensorType.view(shape: IntArray): TensorType
 
+    //https://pytorch.org/docs/stable/generated/torch.abs.html
     public fun TensorType.abs(): TensorType
     public fun TensorType.absAssign(): Unit
+
+    //https://pytorch.org/docs/stable/generated/torch.sum.html
     public fun TensorType.sum(): TensorType
     public fun TensorType.sumAssign(): Unit
 }
 
 // https://proofwiki.org/wiki/Definition:Division_Algebra
-
 public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>> :
     TensorAlgebra<T, TensorType> {
 
     public operator fun TensorType.div(other: TensorType): TensorType
     public operator fun TensorType.divAssign(other: TensorType)
 
+    //https://pytorch.org/docs/stable/generated/torch.exp.html
     public fun TensorType.exp(): TensorType
     public fun TensorType.expAssign(): Unit
+
+    //https://pytorch.org/docs/stable/generated/torch.log.html
     public fun TensorType.log(): TensorType
     public fun TensorType.logAssign(): Unit
 
+    //https://pytorch.org/docs/stable/generated/torch.svd.html
     public fun TensorType.svd(): Triple<TensorType, TensorType, TensorType>
+
+    //https://pytorch.org/docs/stable/generated/torch.symeig.html
     public fun TensorType.symEig(eigenvectors: Boolean = true): Pair<TensorType, TensorType>
 
-}
\ No newline at end of file
+}
+
+public inline fun <T, TensorType : TensorStructure<T>,
+        TorchTensorAlgebraType : TensorAlgebra<T, TensorType>>
+        TorchTensorAlgebraType.checkShapeCompatible(
+    a: TensorType, b: TensorType
+): Unit =
+    check(a.shape contentEquals b.shape) {
+        "Tensors must be of identical shape"
+    }
+
+public inline fun <T, TensorType : TensorStructure<T>,
+        TorchTensorAlgebraType : TensorAlgebra<T, TensorType>>
+        TorchTensorAlgebraType.checkDot(a: TensorType, b: TensorType): Unit {
+    val sa = a.shape
+    val sb = b.shape
+    val na = sa.size
+    val nb = sb.size
+    var status: Boolean
+    if (nb == 1) {
+        status = sa.last() == sb[0]
+    } else {
+        status = sa.last() == sb[nb - 2]
+        if ((na > 2) and (nb > 2)) {
+            status = status and
+                    (sa.take(nb - 2).toIntArray() contentEquals sb.take(nb - 2).toIntArray())
+        }
+    }
+    check(status) { "Incompatible shapes $sa and $sb for dot product" }
+}
+
+public inline fun <T, TensorType : TensorStructure<T>,
+        TorchTensorAlgebraType : TensorAlgebra<T, TensorType>>
+        TorchTensorAlgebraType.checkTranspose(dim: Int, i: Int, j: Int): Unit =
+    check((i < dim) and (j < dim)) {
+        "Cannot transpose $i to $j for a tensor of dim $dim"
+    }
+
+public inline fun <T, TensorType : TensorStructure<T>,
+        TorchTensorAlgebraType : TensorAlgebra<T, TensorType>>
+        TorchTensorAlgebraType.checkView(a: TensorType, shape: IntArray): Unit =
+    check(a.shape.reduce(Int::times) == shape.reduce(Int::times))
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
new file mode 100644
index 000000000..822e514d5
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
@@ -0,0 +1,50 @@
+package space.kscience.kmath.tensors
+
+import space.kscience.kmath.nd.Strides
+import space.kscience.kmath.nd.offsetFromIndex
+import kotlin.math.max
+
+
+inline public fun stridesFromShape(shape: IntArray): IntArray {
+    val nDim = shape.size
+    val res = IntArray(nDim)
+    if (nDim == 0)
+        return res
+
+    var current = nDim - 1
+    res[current] = 1
+
+    while (current > 0) {
+        res[current - 1] = max(1, shape[current]) * res[current]
+        current--
+    }
+    return res
+
+}
+
+inline public fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArray {
+    val res = IntArray(nDim)
+    var current = offset
+    var strideIndex = 0
+
+    while (strideIndex < nDim) {
+        res[strideIndex] = (current / strides[strideIndex])
+        current %= strides[strideIndex]
+        strideIndex++
+    }
+    return res
+}
+
+
+public class TensorStrides(override val shape: IntArray) : Strides {
+    override val strides: IntArray
+        get() = stridesFromShape(shape)
+
+    override fun offset(index: IntArray): Int = offsetFromIndex(index, shape, strides)
+
+    override fun index(offset: Int): IntArray =
+        indexFromOffset(offset, strides, shape.size)
+
+    override val linearSize: Int
+        get() = shape.fold(1) { acc, i -> acc * i }
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStructure.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStructure.kt
new file mode 100644
index 000000000..6d2d855b6
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStructure.kt
@@ -0,0 +1,23 @@
+package space.kscience.kmath.tensors
+
+import space.kscience.kmath.nd.MutableNDStructure
+
+public interface TensorStructure<T> : MutableNDStructure<T> {
+    public fun item(): T
+
+    // A tensor can have empty shape, in which case it represents just a value
+    public fun value(): T {
+        checkIsValue()
+        return item()
+    }
+}
+
+public inline fun <T> TensorStructure<T>.isValue(): Boolean {
+    return (dimension == 0)
+}
+
+public inline fun <T> TensorStructure<T>.isNotValue(): Boolean = !this.isValue()
+
+public inline fun <T> TensorStructure<T>.checkIsValue(): Unit = check(this.isValue()) {
+    "This tensor has shape ${shape.toList()}"
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensor.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensor.kt
new file mode 100644
index 000000000..7938eb864
--- /dev/null
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensor.kt
@@ -0,0 +1,24 @@
+package space.kscience.kmath.tensors
+
+
+import space.kscience.kmath.structures.array
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.assertTrue
+
+class TestRealTensor {
+
+    @Test
+    fun valueTest(){
+        val value = 12.5
+        val tensor = RealTensor(IntArray(0), doubleArrayOf(value))
+        assertEquals(tensor.value(), value)
+    }
+
+    @Test
+    fun stridesTest(){
+        val tensor = RealTensor(intArrayOf(2,2), doubleArrayOf(3.5,5.8,58.4,2.4))
+        assertEquals(tensor[intArrayOf(0,1)], 5.8)
+        assertTrue(tensor.elements().map{ it.second }.toList().toDoubleArray() contentEquals tensor.buffer.array)
+    }
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
new file mode 100644
index 000000000..86caa0338
--- /dev/null
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
@@ -0,0 +1,16 @@
+package space.kscience.kmath.tensors
+
+import space.kscience.kmath.structures.array
+import kotlin.test.Test
+import kotlin.test.assertTrue
+
+class TestRealTensorAlgebra {
+
+    @Test
+    fun doublePlus() = RealTensorAlgebra {
+        val tensor = RealTensor(intArrayOf(2), doubleArrayOf(1.0, 2.0))
+        val res = 10.0 + tensor
+        assertTrue(res.buffer.array contentEquals doubleArrayOf(11.0,12.0))
+    }
+
+}
\ No newline at end of file
diff --git a/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/Device.kt b/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/Device.kt
index 8c086c396..6b74212ea 100644
--- a/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/Device.kt
+++ b/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/Device.kt
@@ -10,13 +10,13 @@ public sealed class Device {
     public data class CUDA(val index: Int): Device()
     public fun toInt(): Int {
         when(this) {
-            is Device.CPU -> return 0
-            is Device.CUDA -> return this.index + 1
+            is CPU -> return 0
+            is CUDA -> return this.index + 1
         }
     }
     public companion object {
         public fun fromInt(deviceInt: Int): Device {
-            return if (deviceInt == 0) Device.CPU else Device.CUDA(
+            return if (deviceInt == 0) CPU else CUDA(
                 deviceInt - 1
             )
         }
diff --git a/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensor.kt b/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensor.kt
index 8175f0009..0cda1a375 100644
--- a/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensor.kt
+++ b/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensor.kt
@@ -2,17 +2,14 @@
 
 package space.kscience.kmath.torch
 
-import space.kscience.kmath.tensors.TensorStructure
+import space.kscience.kmath.tensors.*
 
 public interface TorchTensor<T> : TensorStructure<T> {
-    public fun item(): T
+
     public val strides: IntArray
     public val size: Int
     public val device: Device
-    override fun value(): T {
-        checkIsValue()
-        return item()
-    }
+
     override fun elements(): Sequence<Pair<IntArray, T>> {
         if (dimension == 0) {
             return emptySequence()
@@ -22,31 +19,8 @@ public interface TorchTensor<T> : TensorStructure<T> {
     }
 }
 
-public inline fun <T> TorchTensor<T>.isValue(): Boolean {
-    return (dimension == 0)
-}
-
-public inline fun <T> TorchTensor<T>.isNotValue(): Boolean = !this.isValue()
-
-public inline fun <T> TorchTensor<T>.checkIsValue(): Unit = check(this.isValue()) {
-    "This tensor has shape ${shape.toList()}"
-}
-
 public interface TorchTensorOverField<T>: TorchTensor<T>
 {
     public var requiresGrad: Boolean
 }
 
-private inline fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArray {
-    val res = IntArray(nDim)
-    var current = offset
-    var strideIndex = 0
-
-    while (strideIndex < nDim) {
-        res[strideIndex] = (current / strides[strideIndex])
-        current %= strides[strideIndex]
-        strideIndex++
-    }
-    return res
-}
-
diff --git a/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebra.kt b/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebra.kt
index 9def17c8e..ac760d109 100644
--- a/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebra.kt
+++ b/kmath-torch/src/commonMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebra.kt
@@ -2,8 +2,7 @@
 
 package space.kscience.kmath.torch
 
-import space.kscience.kmath.tensors.TensorAlgebra
-import space.kscience.kmath.tensors.TensorPartialDivisionAlgebra
+import space.kscience.kmath.tensors.*
 
 public interface TorchTensorAlgebra<T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>> :
     TensorAlgebra<T, TorchTensorType> {
@@ -75,15 +74,6 @@ public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
         "Tensors must be on the same device"
     }
 
-public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
-        TorchTensorAlgebraType : TorchTensorAlgebra<T, PrimitiveArrayType, TorchTensorType>>
-        TorchTensorAlgebraType.checkShapeCompatible(
-    a: TorchTensorType,
-    b: TorchTensorType
-): Unit =
-    check(a.shape contentEquals b.shape) {
-        "Tensors must be of identical shape"
-    }
 
 public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
         TorchTensorAlgebraType : TorchTensorAlgebra<T, PrimitiveArrayType, TorchTensorType>>
@@ -92,8 +82,8 @@ public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
     b: TorchTensorType
 ) {
     if (a.isNotValue() and b.isNotValue()) {
-        this.checkDeviceCompatible(a, b)
-        this.checkShapeCompatible(a, b)
+        checkDeviceCompatible(a, b)
+        checkShapeCompatible(a, b)
     }
 }
 
@@ -101,36 +91,9 @@ public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
         TorchTensorAlgebraType : TorchTensorAlgebra<T, PrimitiveArrayType, TorchTensorType>>
         TorchTensorAlgebraType.checkDotOperation(a: TorchTensorType, b: TorchTensorType): Unit {
     checkDeviceCompatible(a, b)
-    val sa = a.shape
-    val sb = b.shape
-    val na = sa.size
-    val nb = sb.size
-    var status: Boolean
-    if (nb == 1) {
-        status = sa.last() == sb[0]
-    } else {
-        status = sa.last() == sb[nb - 2]
-        if ((na > 2) and (nb > 2)) {
-            status = status and
-                    (sa.take(nb - 2).toIntArray() contentEquals sb.take(nb - 2).toIntArray())
-        }
-    }
-    check(status) { "Incompatible shapes $sa and $sb for dot product" }
+    checkDot(a,b)
 }
 
-public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
-        TorchTensorAlgebraType : TorchTensorAlgebra<T, PrimitiveArrayType, TorchTensorType>>
-        TorchTensorAlgebraType.checkTranspose(dim: Int, i: Int, j: Int): Unit =
-    check((i < dim) and (j < dim)) {
-        "Cannot transpose $i to $j for a tensor of dim $dim"
-    }
-
-public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensor<T>,
-        TorchTensorAlgebraType : TorchTensorAlgebra<T, PrimitiveArrayType, TorchTensorType>>
-        TorchTensorAlgebraType.checkView(a: TorchTensorType, shape: IntArray): Unit =
-    check(a.shape.reduce(Int::times) == shape.reduce(Int::times))
-
-
 public inline fun <T, PrimitiveArrayType, TorchTensorType : TorchTensorOverField<T>,
         TorchTensorDivisionAlgebraType : TorchTensorPartialDivisionAlgebra<T, PrimitiveArrayType, TorchTensorType>>
         TorchTensorDivisionAlgebraType.withGradAt(
diff --git a/kmath-torch/src/jvmMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraJVM.kt b/kmath-torch/src/jvmMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraJVM.kt
index a11ed9cad..9c77b8229 100644
--- a/kmath-torch/src/jvmMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraJVM.kt
+++ b/kmath-torch/src/jvmMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraJVM.kt
@@ -29,9 +29,9 @@ public sealed class TorchTensorAlgebraJVM<
 
     internal abstract fun wrap(tensorHandle: Long): TorchTensorType
 
-    override operator fun TorchTensorType.times(other: TorchTensorType): TorchTensorType {
-        if (checks) checkLinearOperation(this, other)
-        return wrap(JTorch.timesTensor(this.tensorHandle, other.tensorHandle))
+    override operator fun TorchTensorType.times(b: TorchTensorType): TorchTensorType {
+        if (checks) checkLinearOperation(this, b)
+        return wrap(JTorch.timesTensor(this.tensorHandle, b.tensorHandle))
     }
 
     override operator fun TorchTensorType.timesAssign(other: TorchTensorType): Unit {
@@ -39,9 +39,9 @@ public sealed class TorchTensorAlgebraJVM<
         JTorch.timesTensorAssign(this.tensorHandle, other.tensorHandle)
     }
 
-    override operator fun TorchTensorType.plus(other: TorchTensorType): TorchTensorType {
-        if (checks) checkLinearOperation(this, other)
-        return wrap(JTorch.plusTensor(this.tensorHandle, other.tensorHandle))
+    override operator fun TorchTensorType.plus(b: TorchTensorType): TorchTensorType {
+        if (checks) checkLinearOperation(this, b)
+        return wrap(JTorch.plusTensor(this.tensorHandle, b.tensorHandle))
     }
 
     override operator fun TorchTensorType.plusAssign(other: TorchTensorType): Unit {
@@ -49,9 +49,9 @@ public sealed class TorchTensorAlgebraJVM<
         JTorch.plusTensorAssign(this.tensorHandle, other.tensorHandle)
     }
 
-    override operator fun TorchTensorType.minus(other: TorchTensorType): TorchTensorType {
-        if (checks) checkLinearOperation(this, other)
-        return wrap(JTorch.minusTensor(this.tensorHandle, other.tensorHandle))
+    override operator fun TorchTensorType.minus(b: TorchTensorType): TorchTensorType {
+        if (checks) checkLinearOperation(this, b)
+        return wrap(JTorch.minusTensor(this.tensorHandle, b.tensorHandle))
     }
 
     override operator fun TorchTensorType.minusAssign(other: TorchTensorType): Unit {
diff --git a/kmath-torch/src/nativeMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraNative.kt b/kmath-torch/src/nativeMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraNative.kt
index 3aba636e9..5f5515680 100644
--- a/kmath-torch/src/nativeMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraNative.kt
+++ b/kmath-torch/src/nativeMain/kotlin/space/kscience/kmath/torch/TorchTensorAlgebraNative.kt
@@ -1,10 +1,10 @@
 package space.kscience.kmath.torch
 
-
 import space.kscience.kmath.memory.DeferScope
 import space.kscience.kmath.memory.withDeferScope
 
 import kotlinx.cinterop.*
+import space.kscience.kmath.tensors.*
 import space.kscience.kmath.torch.ctorch.*
 
 public sealed class TorchTensorAlgebraNative<
@@ -38,9 +38,9 @@ public sealed class TorchTensorAlgebraNative<
     public abstract fun fromBlob(arrayBlob: CPointer<TVar>, shape: IntArray): TorchTensorType
     public abstract fun TorchTensorType.getData(): CPointer<TVar>
 
-    override operator fun TorchTensorType.times(other: TorchTensorType): TorchTensorType {
-        if (checks) checkLinearOperation(this, other)
-        return wrap(times_tensor(this.tensorHandle, other.tensorHandle)!!)
+    override operator fun TorchTensorType.times(b: TorchTensorType): TorchTensorType {
+        if (checks) checkLinearOperation(this, b)
+        return wrap(times_tensor(this.tensorHandle, b.tensorHandle)!!)
     }
 
     override operator fun TorchTensorType.timesAssign(other: TorchTensorType): Unit {
@@ -48,9 +48,9 @@ public sealed class TorchTensorAlgebraNative<
         times_tensor_assign(this.tensorHandle, other.tensorHandle)
     }
 
-    override operator fun TorchTensorType.plus(other: TorchTensorType): TorchTensorType {
-        if (checks) checkLinearOperation(this, other)
-        return wrap(plus_tensor(this.tensorHandle, other.tensorHandle)!!)
+    override operator fun TorchTensorType.plus(b: TorchTensorType): TorchTensorType {
+        if (checks) checkLinearOperation(this, b)
+        return wrap(plus_tensor(this.tensorHandle, b.tensorHandle)!!)
     }
 
     override operator fun TorchTensorType.plusAssign(other: TorchTensorType): Unit {
@@ -58,9 +58,9 @@ public sealed class TorchTensorAlgebraNative<
         plus_tensor_assign(this.tensorHandle, other.tensorHandle)
     }
 
-    override operator fun TorchTensorType.minus(other: TorchTensorType): TorchTensorType {
-        if (checks) checkLinearOperation(this, other)
-        return wrap(minus_tensor(this.tensorHandle, other.tensorHandle)!!)
+    override operator fun TorchTensorType.minus(b: TorchTensorType): TorchTensorType {
+        if (checks) checkLinearOperation(this, b)
+        return wrap(minus_tensor(this.tensorHandle, b.tensorHandle)!!)
     }
 
     override operator fun TorchTensorType.minusAssign(other: TorchTensorType): Unit {
@@ -68,6 +68,10 @@ public sealed class TorchTensorAlgebraNative<
         minus_tensor_assign(this.tensorHandle, other.tensorHandle)
     }
 
+    override fun add(a: TorchTensorType, b: TorchTensorType): TorchTensorType = a + b
+
+    override fun multiply(a: TorchTensorType, b: TorchTensorType): TorchTensorType = a * b
+
     override operator fun TorchTensorType.unaryMinus(): TorchTensorType =
         wrap(unary_minus(this.tensorHandle)!!)
 
@@ -254,6 +258,15 @@ public class TorchTensorRealAlgebra(scope: DeferScope) :
 
     override fun full(value: Double, shape: IntArray, device: Device): TorchTensorReal =
         wrap(full_double(value, shape.toCValues(), shape.size, device.toInt())!!)
+
+
+    override fun multiply(a: TorchTensorReal, k: Number): TorchTensorReal = a * k.toDouble()
+
+    override val zero: TorchTensorReal
+        get() = full(0.0, IntArray(0), Device.CPU)
+
+    override val one: TorchTensorReal
+        get() = full(1.0, IntArray(0), Device.CPU)
 }
 
 
@@ -317,6 +330,15 @@ public class TorchTensorFloatAlgebra(scope: DeferScope) :
     override fun full(value: Float, shape: IntArray, device: Device): TorchTensorFloat =
         wrap(full_float(value, shape.toCValues(), shape.size, device.toInt())!!)
 
+    override fun multiply(a: TorchTensorFloat, k: Number): TorchTensorFloat = a * k.toFloat()
+
+    override val zero: TorchTensorFloat
+        get() = full(0f, IntArray(0), Device.CPU)
+
+
+    override val one: TorchTensorFloat
+        get() = full(1f, IntArray(0), Device.CPU)
+
 }
 
 public class TorchTensorLongAlgebra(scope: DeferScope) :
@@ -372,6 +394,15 @@ public class TorchTensorLongAlgebra(scope: DeferScope) :
 
     override fun full(value: Long, shape: IntArray, device: Device): TorchTensorLong =
         wrap(full_long(value, shape.toCValues(), shape.size, device.toInt())!!)
+
+    override fun multiply(a: TorchTensorLong, k: Number): TorchTensorLong = a * k.toLong()
+
+    override val zero: TorchTensorLong
+        get() = full(0, IntArray(0), Device.CPU)
+
+
+    override val one: TorchTensorLong
+        get() = full(1, IntArray(0), Device.CPU)
 }
 
 public class TorchTensorIntAlgebra(scope: DeferScope) :
@@ -427,6 +458,16 @@ public class TorchTensorIntAlgebra(scope: DeferScope) :
 
     override fun full(value: Int, shape: IntArray, device: Device): TorchTensorInt =
         wrap(full_int(value, shape.toCValues(), shape.size, device.toInt())!!)
+
+
+    override fun multiply(a: TorchTensorInt, k: Number): TorchTensorInt = a * k.toInt()
+
+    override val zero: TorchTensorInt
+        get() = full(0, IntArray(0), Device.CPU)
+
+
+    override val one: TorchTensorInt
+        get() = full(1, IntArray(0), Device.CPU)
 }