Tensor/matrix operations

Transpose

Transpose is an important operation defined for matrices or tensors. For a matrix, the transpose is defined as follows:

Here, A^T denotes the transpose of A.

An example of the transpose operation can be illustrated as follows:

After the transpose operation:

For a tensor, transpose can be seen as permuting the dimensions order. For example, let’s define a tensor S, as shown here:

Now one transpose operation (out of many) can be defined as follows:

Matrix multiplication

Matrix multiplication is another important operation that appears quite frequently in linear algebra.

Given the matrices and , the multiplication of A and B is defined as follows:

Here, .

Consider this example:

This gives , and the value of C is as follows:

Element-wise multiplication

Element-wise matrix multiplication (or the Hadamard product) is computed for two matrices...