Matrices Pt 1

A matrix is made up of a grid of real numbers, the grid can be r rows and c columns. If a matrix has 3 rows and 2 columns it is referred to as a 3x2 matrix. A matrix is typically expressed by a capital letter. These can be used to make changes or transform a vector or position in video games. There are two ways to declare a matrix

Method 1

Method 2

Identity Matrix
The identity matrix is a matrix with equal number of rows and columns to another matrix, as well as this each component of the identity matrix is 0, except for a diagonal of 1s that start in the top left and works its way down.

Addition & Subtraction
In order to add or subtract two matrices they have to have the same dimensions or in other words, the amount of rows must match and the amount of columns must match. When adding two matrices we simply add each corresponding component together.

The same goes for subtraction as we subtract each corresponding component from one another.

Matrix Equations
Matrix equations are equations where a matrix is being represented by a letter, similarly to how you might have the equation 5x = 15, which when solved gives x = 3.

An example of this is below, where we have to find A.

The first step is to get A on its own.

Then we carry out the matrix subtraction to give us the value of A.

Scalar Multiplication
This is the same as scalar multiplication of vectors as each component of the matrix is multiplied by the scalar value.

Zero Matrices

A zero matrix is a matrix which has ever element as a value of 0. A zero matrix is represented with a 0 like below and the dimensions are subscripted to that 0.

When you add a zero matrix to any matrix you get the original matrix, whereas if you add the opposite of a matrix to the original matrix you get the zero matrix. If you multiply a matrix by zero you get a zero matrix that has the same dimensions as the original.

All images were created using https://www.codecogs.com/latex/eqneditor.php