Data operations

In this section, we will look at some of the most common transformations applied on matrices.

• Matrix transpose: Matrix transpose is a matrix transform that simply mirrors the matrix along its main diagonal. Mathematically it is defined as follows: 

• Matrix multiplication: Matrix multiplication is one of the most fundamental operations that can be applied to any two matrices. A matrix, A, of shape A_r x A_c can be multiplied by another matrix, B, of shape B_r x B_c if and only if A_c = B_r. The resultant matrix, C, is the shape A_r x B_c .The multiplication operation is defined as follows:

Matrix multiplication generally has very useful properties. For example, matrix multiplication is distributive:

                Matrix multiplication is also associative:

               Matrix multiplication also has a very simple form for its transpose:

Matrix multiplication is not commutative, which means A x B ≠ B x A. However, the dot products between two vectors is commutative: