Introduction to Matrix Multiplication

This is a brief explanation of matrix multiplication for those who are not familiar with it. So long as you understand how to add and multiply you can understand matrix multiplication – it is really no more difficult than a Sudoku puzzle.

Consider the following matrix and vector, which are to be multiplied:

The matrix elements are labelled by row then column, hence is the element in the r'th row and the c'th column.

To explain matrix multiplication step by step, first take the top row and rotate it into a column vector then align it with the vector v:

We then multiply the correspond vector elements giving us:

Then we sum these elements together into a single value then assign this value to the top element of a new vector n:

Once we have done this for each row in the matrix we have a new vector n:

This is nothing more than a structured process of multiplication and addition. With a little practice it can become very easy to comprehend.


Another way to visualise the process is to take the vector and rotate it then place it above the matrix:

Then let the vector elements slide down to a row, combine with the row elements and slide off to the right to form a new vector element. 14th Sept 2008