Matrices

Matrices are two dimensional arrays of numbers, e.g.

\[ \begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix} \]

describes a 3 by 2 matrix.

A matrix is described by the number of rows, then the number of columns.

Matrix Multiplication

Matrix Multiplication is the process of multiplying two compatible matrices together. Unlike scalar multiplication, matrix multiplication is not commutative - that is, if a and b are matrices, \(a * b\) is not guaranteed to produce the same matrix that \(b * a\) produces.

In order to be compatible, the number of columns in matrix a must equal the number of rows in matrix b. This will produce a matrix that has the same number of rows as matrix a and the same number of columns as matrix b.

See this explanation until I write up a better one.

Note that this is also called the dot product.