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 3e21a3a98..9e040fcd8 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 +3,7 @@ package space.kscience.kmath.tensors
 import space.kscience.kmath.structures.RealBuffer
 import space.kscience.kmath.structures.array
 import kotlin.math.abs
+import kotlin.math.max
 
 
 public class RealTensor(
@@ -50,27 +51,85 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
         return RealTensor(this.shape, this.buffer.array.copyOf())
     }
 
+    override fun broadcastShapes(vararg shapes: IntArray): IntArray {
+        var totalDim = 0
+        for (shape in shapes) {
+            totalDim = max(totalDim, shape.size)
+        }
+
+        val totalShape = IntArray(totalDim) {0}
+        for (shape in shapes) {
+            for (i in shape.indices) {
+                val curDim = shape[i]
+                val offset = totalDim - shape.size
+                totalShape[i + offset] = max(totalShape[i + offset], curDim)
+            }
+        }
+
+        for (shape in shapes) {
+            for (i in shape.indices) {
+                val curDim = shape[i]
+                val offset = totalDim - shape.size
+                if (curDim != 1 && totalShape[i + offset] != curDim) {
+                    throw RuntimeException("Shapes are not compatible and cannot be broadcast")
+                }
+            }
+        }
+
+        return totalShape
+    }
+
+    override fun broadcastTensors(vararg tensors: RealTensor): List<RealTensor> {
+        val totalShape = broadcastShapes(*(tensors.map { it.shape }).toTypedArray())
+        val n = totalShape.reduce{ acc, i ->  acc * i }
+
+        val res = ArrayList<RealTensor>(0)
+        for (tensor in tensors) {
+            val resTensor = RealTensor(totalShape, DoubleArray(n))
+
+            for (linearIndex in 0 until n) {
+                val totalMultiIndex = resTensor.strides.index(linearIndex)
+                val curMultiIndex = tensor.shape.copyOf()
+
+                val offset = totalMultiIndex.size - curMultiIndex.size
+
+                for (i in curMultiIndex.indices) {
+                    if (curMultiIndex[i] != 1) {
+                        curMultiIndex[i] = totalMultiIndex[i + offset]
+                    } else {
+                        curMultiIndex[i] = 0
+                    }
+                }
+
+                val curLinearIndex = tensor.strides.offset(curMultiIndex)
+                resTensor.buffer.array[linearIndex] = tensor.buffer.array[curLinearIndex]
+            }
+            res.add(resTensor)
+        }
+
+        return res
+    }
+
     override fun Double.plus(other: RealTensor): RealTensor {
-        //todo should be change with broadcasting
         val resBuffer = DoubleArray(other.buffer.size) { i ->
             other.buffer.array[i] + this
         }
         return RealTensor(other.shape, resBuffer)
     }
 
-    //todo should be change with broadcasting
     override fun RealTensor.plus(value: Double): RealTensor = value + this
 
     override fun RealTensor.plus(other: RealTensor): RealTensor {
-        //todo should be change with broadcasting
-        val resBuffer = DoubleArray(this.buffer.size) { i ->
-            this.buffer.array[i] + other.buffer.array[i]
+        val broadcast = broadcastTensors(this, other)
+        val newThis = broadcast[0]
+        val newOther = broadcast[1]
+        val resBuffer = DoubleArray(newThis.buffer.size) { i ->
+            newThis.buffer.array[i] + newOther.buffer.array[i]
         }
-        return RealTensor(this.shape, resBuffer)
+        return RealTensor(newThis.shape, resBuffer)
     }
 
     override fun RealTensor.plusAssign(value: Double) {
-        //todo should be change with broadcasting
         for (i in this.buffer.array.indices) {
             this.buffer.array[i] += value
         }
@@ -84,19 +143,33 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun Double.minus(other: RealTensor): RealTensor {
-        TODO("Alya")
+        val resBuffer = DoubleArray(other.buffer.size) { i ->
+            this - other.buffer.array[i]
+        }
+        return RealTensor(other.shape, resBuffer)
     }
 
     override fun RealTensor.minus(value: Double): RealTensor {
-        TODO("Alya")
+        val resBuffer = DoubleArray(this.buffer.size) { i ->
+            this.buffer.array[i] - value
+        }
+        return RealTensor(this.shape, resBuffer)
     }
 
     override fun RealTensor.minus(other: RealTensor): RealTensor {
-        TODO("Alya")
+        val broadcast = broadcastTensors(this, other)
+        val newThis = broadcast[0]
+        val newOther = broadcast[1]
+        val resBuffer = DoubleArray(newThis.buffer.size) { i ->
+            newThis.buffer.array[i] - newOther.buffer.array[i]
+        }
+        return RealTensor(newThis.shape, resBuffer)
     }
 
     override fun RealTensor.minusAssign(value: Double) {
-        TODO("Alya")
+        for (i in this.buffer.array.indices) {
+            this.buffer.array[i] -= value
+        }
     }
 
     override fun RealTensor.minusAssign(other: RealTensor) {
@@ -147,19 +220,12 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
         TODO("Alya")
     }
 
-    override fun RealTensor.dotAssign(other: RealTensor) {
-        TODO("Alya")
-    }
-
-    override fun RealTensor.dotRightAssign(other: RealTensor) {
-        TODO("Alya")
-    }
-
     override fun diagonalEmbedding(diagonalEntries: RealTensor, offset: Int, dim1: Int, dim2: Int): RealTensor {
         TODO("Alya")
     }
 
     override fun RealTensor.transpose(i: Int, j: Int): RealTensor {
+        checkTranspose(this.dimension, i, j)
         val n = this.buffer.size
         val resBuffer = DoubleArray(n)
 
@@ -179,15 +245,6 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
         return resTensor
     }
 
-    override fun RealTensor.transposeAssign(i: Int, j: Int) {
-        val transposedTensor = this.transpose(i, j)
-        for (i in transposedTensor.shape.indices) {
-            this.shape[i] = transposedTensor.shape[i]
-        }
-        for (i in transposedTensor.buffer.array.indices) {
-            this.buffer.array[i] = transposedTensor.buffer.array[i]
-        }
-    }
 
     override fun RealTensor.view(shape: IntArray): RealTensor {
         return RealTensor(shape, this.buffer.array)
@@ -201,17 +258,12 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, 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(value: Double): RealTensor {
         TODO("Not yet implemented")
@@ -233,17 +285,10 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, 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.lu(): Pair<RealTensor, IntTensor> {
         // todo checks
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 0dbcae044..ec257e45c 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
@@ -13,6 +13,9 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 
     public fun TensorType.copy(): TensorType
 
+    public fun broadcastShapes(vararg shapes: IntArray): IntArray
+    public fun broadcastTensors(vararg tensors: RealTensor): List<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
@@ -35,8 +38,6 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 
     //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(
@@ -46,7 +47,6 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 
     //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
@@ -54,11 +54,9 @@ public interface TensorAlgebra<T, TensorType : TensorStructure<T>> {
 
     //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
@@ -72,11 +70,9 @@ public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>
 
     //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
 
     // todo change type of pivots
     //https://pytorch.org/docs/stable/generated/torch.lu.html
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
index 8e95922b8..c9fd6bb3a 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
@@ -2,6 +2,8 @@ package space.kscience.kmath.tensors
 
 import space.kscience.kmath.structures.array
 import kotlin.test.Test
+import kotlin.test.assertFails
+import kotlin.test.assertFailsWith
 import kotlin.test.assertTrue
 
 class TestRealTensorAlgebra {
@@ -48,20 +50,48 @@ class TestRealTensorAlgebra {
     }
 
     @Test
-    fun transposeAssign1x2() = RealTensorAlgebra {
-        val tensor = RealTensor(intArrayOf(1,2), doubleArrayOf(1.0, 2.0))
-        tensor.transposeAssign(0, 1)
+    fun broadcastShapes() = RealTensorAlgebra {
+        assertTrue(this.broadcastShapes(
+            intArrayOf(2, 3), intArrayOf(1, 3), intArrayOf(1, 1, 1)
+        ) contentEquals intArrayOf(1, 2, 3))
 
-        assertTrue(tensor.buffer.array contentEquals doubleArrayOf(1.0, 2.0))
-        assertTrue(tensor.shape contentEquals intArrayOf(2, 1))
+        assertTrue(this.broadcastShapes(
+            intArrayOf(6, 7), intArrayOf(5, 6, 1), intArrayOf(7,), intArrayOf(5, 1, 7)
+        ) contentEquals intArrayOf(5, 6, 7))
     }
 
     @Test
-    fun transposeAssign2x3() = RealTensorAlgebra {
-        val tensor = RealTensor(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
-        tensor.transposeAssign(1, 0)
+    fun broadcastTensors() = RealTensorAlgebra {
+        val tensor1 = RealTensor(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val tensor2 = RealTensor(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
+        val tensor3 = RealTensor(intArrayOf(1, 1, 1), doubleArrayOf(500.0))
 
-        assertTrue(tensor.buffer.array contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
-        assertTrue(tensor.shape contentEquals intArrayOf(3, 2))
+        val res = this.broadcastTensors(tensor1, tensor2, tensor3)
+
+        assertTrue(res[0].shape contentEquals intArrayOf(1, 2, 3))
+        assertTrue(res[1].shape contentEquals intArrayOf(1, 2, 3))
+        assertTrue(res[2].shape contentEquals intArrayOf(1, 2, 3))
+
+        assertTrue(res[0].buffer.array contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        assertTrue(res[1].buffer.array contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0))
+        assertTrue(res[2].buffer.array contentEquals doubleArrayOf(500.0, 500.0, 500.0, 500.0, 500.0, 500.0))
     }
+
+    @Test
+    fun minusTensor() = RealTensorAlgebra {
+        val tensor1 = RealTensor(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val tensor2 = RealTensor(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
+        val tensor3 = RealTensor(intArrayOf(1, 1, 1), doubleArrayOf(500.0))
+
+        assertTrue((tensor2 - tensor1).shape contentEquals intArrayOf(2, 3))
+        assertTrue((tensor2 - tensor1).buffer.array contentEquals doubleArrayOf(9.0, 18.0, 27.0, 6.0, 15.0, 24.0))
+
+        assertTrue((tensor3 - tensor1).shape contentEquals intArrayOf(1, 2, 3))
+        assertTrue((tensor3 - tensor1).buffer.array
+                contentEquals doubleArrayOf(499.0, 498.0, 497.0, 496.0, 495.0, 494.0))
+
+        assertTrue((tensor3 - tensor2).shape contentEquals intArrayOf(1, 1, 3))
+        assertTrue((tensor3 - tensor2).buffer.array contentEquals doubleArrayOf(490.0, 480.0, 470.0))
+    }
+
 }
\ No newline at end of file