Matrices & Linear Transformations
A matrix is a system of elements within a pair of brackets. The size of the matrix is given as the number of rows and columns in it.
A square matrix is one where there is an equal number of rows and columns
A zero matrix is one in which all the elements are zero
An identity matrix is a square matrix where the all the values on the diagonal from top left to bottom right are 1, and all other values are zero. This is noted as capital i, I with a subscript number afterwards to show its size.
Working with Matrices
Adding and Subtracting
To add or subtract matrices, you add or subtract the corresponding elements in each matrix.
You can only add or subtract matrices of the same size
Multiplying by a Scalar
To multiple a vector by a scalar, simply multiple each element in the vector by the scalar. This can be factorised out, too.
Multiplying One Vector by Another
Matrix multiplication is only possible if the number of columns in the first matrix equals the number of rows in the second matrix. The result of the multiplication is known as the product matrix, and will have the same number of rows as the first matrix and the same number of columns as the second matrix.
Order of matrix multiplication matters
For two matrices, A and B:
In general, AB ≠ BA<