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
index cad01c4d0..13c57fc18 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
@@ -3,6 +3,8 @@ package space.kscience.kmath.tensors
 import space.kscience.kmath.nd.MutableNDBuffer
 import space.kscience.kmath.structures.RealBuffer
 import space.kscience.kmath.structures.array
+import kotlin.js.JsName
+import kotlin.math.abs
 
 
 public class RealTensor(
@@ -13,46 +15,80 @@ public class RealTensor(
     MutableNDBuffer<Double>(
         TensorStrides(shape),
         RealBuffer(buffer)
-    ) {
-    /*
-     * TODO: Andrei remove item()
-     */
-    override fun item(): Double {
-        check(buffer.size > 0) { "The tensor is empty" }
-        return buffer[0]
-    }
-}
-
+    )
 
 public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor> {
 
+    //rename to item?
     override fun RealTensor.value(): Double {
-        TODO("Andrei")
+        check(this.dimension == 0) {
+            // todo change message
+            "This tensor has shape ${shape.toList()}"
+        }
+        return this.buffer.array[0]
+    }
+
+    override fun eye(n: Int): RealTensor {
+        val shape = intArrayOf(n, n)
+        val buffer = DoubleArray(n * n) { 0.0 }
+        val res = RealTensor(shape, buffer)
+        for (i in 0 until n) {
+            res[intArrayOf(i, i)] = 1.0
+        }
+        return res
+    }
+
+    override fun zeros(shape: IntArray): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun zeroesLike(other: RealTensor): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun ones(shape: IntArray): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun onesLike(shape: IntArray): RealTensor {
+        TODO("Not yet implemented")
+    }
+
+    override fun RealTensor.copy(): RealTensor {
+        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)
+        //todo should be change with broadcasting
+        val resBuffer = DoubleArray(other.buffer.size) { i ->
+            other.buffer.array[i] + this
+        }
+        return RealTensor(other.shape, resBuffer)
     }
 
-    override fun RealTensor.plus(value: Double): RealTensor {
-        TODO("Andrei")
-    }
+    //todo should be change with broadcasting
+    override fun RealTensor.plus(value: Double): RealTensor = value + this
 
     override fun RealTensor.plus(other: RealTensor): RealTensor {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        val resBuffer = DoubleArray(this.buffer.size) { i ->
+            this.buffer.array[i] + other.buffer.array[i]
+        }
+        return RealTensor(this.shape, resBuffer)
     }
 
     override fun RealTensor.plusAssign(value: Double) {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        for (i in this.buffer.array.indices) {
+            this.buffer.array[i] += value
+        }
     }
 
     override fun RealTensor.plusAssign(other: RealTensor) {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        for (i in this.buffer.array.indices) {
+            this.buffer.array[i] += other.buffer.array[i]
+        }
     }
 
     override fun Double.minus(other: RealTensor): RealTensor {
@@ -76,27 +112,43 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun Double.times(other: RealTensor): RealTensor {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        val resBuffer = DoubleArray(other.buffer.size) { i ->
+            other.buffer.array[i] * this
+        }
+        return RealTensor(other.shape, resBuffer)
     }
 
-    override fun RealTensor.times(value: Double): RealTensor {
-        TODO("Andrei")
-    }
+    //todo should be change with broadcasting
+    override fun RealTensor.times(value: Double): RealTensor = value * this
 
     override fun RealTensor.times(other: RealTensor): RealTensor {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        val resBuffer = DoubleArray(this.buffer.size) { i ->
+            this.buffer.array[i] * other.buffer.array[i]
+        }
+        return RealTensor(this.shape, resBuffer)
     }
 
     override fun RealTensor.timesAssign(value: Double) {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        for (i in this.buffer.array.indices) {
+            this.buffer.array[i] *= value
+        }
     }
 
     override fun RealTensor.timesAssign(other: RealTensor) {
-        TODO("Andrei")
+        //todo should be change with broadcasting
+        for (i in this.buffer.array.indices) {
+            this.buffer.array[i] *= other.buffer.array[i]
+        }
     }
 
     override fun RealTensor.unaryMinus(): RealTensor {
-        TODO("Andrei")
+        val resBuffer = DoubleArray(this.buffer.size) { i ->
+            this.buffer.array[i].unaryMinus()
+        }
+        return RealTensor(this.shape, resBuffer)
     }
 
     override fun RealTensor.dot(other: RealTensor): RealTensor {
@@ -124,11 +176,11 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun RealTensor.view(shape: IntArray): RealTensor {
-        TODO("Andrei")
+        return RealTensor(shape, this.buffer.array)
     }
 
-    override fun RealTensor.view_as(other: RealTensor): RealTensor {
-        TODO("Andrei")
+    override fun RealTensor.viewAs(other: RealTensor): RealTensor {
+        return this.view(other.shape)
     }
 
     override fun RealTensor.abs(): RealTensor {
@@ -147,10 +199,18 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
         TODO("Not yet implemented")
     }
 
+    override fun RealTensor.div(value: Double): RealTensor {
+        TODO("Not yet implemented")
+    }
+
     override fun RealTensor.div(other: RealTensor): RealTensor {
         TODO("Not yet implemented")
     }
 
+    override fun RealTensor.divAssign(value: Double) {
+        TODO("Not yet implemented")
+    }
+
     override fun RealTensor.divAssign(other: RealTensor) {
         TODO("Not yet implemented")
     }
@@ -172,15 +232,10 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun RealTensor.lu(): Pair<RealTensor, RealTensor> {
-        /**
-         * Main first task for @AndreiKingsley
-         * Compare with the implementation of [LupDecomposition]
-         * and provide a common API
-         */
-        TODO("Not yet implemented")
+        TODO()
     }
 
-    override fun lu_unpack(A_LU: RealTensor, pivots: RealTensor): Triple<RealTensor, RealTensor, RealTensor> {
+    override fun luUnpack(A_LU: RealTensor, pivots: RealTensor): Triple<RealTensor, RealTensor, RealTensor> {
         TODO("Not yet implemented")
     }
 
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 b2586e1e9..6f42623e0 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
@@ -5,6 +5,14 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 
     public fun TensorType.value(): T
 
+    public fun eye(n: Int): TensorType
+    public fun zeros(shape: IntArray): TensorType
+    public fun zeroesLike(other: TensorType): TensorType
+    public fun ones(shape: IntArray): TensorType
+    public fun onesLike(shape: IntArray): TensorType
+
+    public fun TensorType.copy(): 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
@@ -42,7 +50,7 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 
     //https://pytorch.org/docs/stable/tensor_view.html
     public fun TensorType.view(shape: IntArray): TensorType
-    public fun TensorType.view_as(other: TensorType): TensorType
+    public fun TensorType.viewAs(other: TensorType): TensorType
 
     //https://pytorch.org/docs/stable/generated/torch.abs.html
     public fun TensorType.abs(): TensorType
@@ -57,7 +65,9 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>> :
     TensorAlgebra<T, TensorType> {
 
+    public operator fun TensorType.div(value: T): TensorType
     public operator fun TensorType.div(other: TensorType): TensorType
+    public operator fun TensorType.divAssign(value: T)
     public operator fun TensorType.divAssign(other: TensorType)
 
     //https://pytorch.org/docs/stable/generated/torch.exp.html
@@ -72,7 +82,7 @@ public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>
     public fun TensorType.lu(): Pair<TensorType, TensorType>
 
     //https://pytorch.org/docs/stable/generated/torch.lu_unpack.html
-    public fun lu_unpack(A_LU: TensorType, pivots: TensorType): Triple<TensorType, TensorType, TensorType>
+    public fun luUnpack(A_LU: TensorType, pivots: TensorType): Triple<TensorType, TensorType, TensorType>
 
     //https://pytorch.org/docs/stable/generated/torch.svd.html
     public fun TensorType.svd(): Triple<TensorType, TensorType, TensorType>
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
index 3ea8f4bf0..dbaefe907 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
@@ -5,7 +5,7 @@ import space.kscience.kmath.nd.offsetFromIndex
 import kotlin.math.max
 
 
-inline public fun stridesFromShape(shape: IntArray): IntArray {
+public inline fun stridesFromShape(shape: IntArray): IntArray {
     val nDim = shape.size
     val res = IntArray(nDim)
     if (nDim == 0)
@@ -22,7 +22,7 @@ inline public fun stridesFromShape(shape: IntArray): IntArray {
 
 }
 
-inline public fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArray {
+public inline fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArray {
     val res = IntArray(nDim)
     var current = offset
     var strideIndex = 0
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
index 3775ea2e5..5463877ce 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStructure.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStructure.kt
@@ -2,26 +2,5 @@ package space.kscience.kmath.tensors
 
 import space.kscience.kmath.nd.MutableNDStructure
 
-public interface TensorStructure<T> : MutableNDStructure<T> {
+public typealias TensorStructure<T> = MutableNDStructure<T>
 
-    /*
-    * TODO: Andrei remove item() and value()
-     */
-    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