Matrices

Matrices are very similar to vectors in Python, in fact you can use the same functions as you did to interact with vectors on matrices.

Once again we will be using the Numpy module, so make sure it is imported

import numpy as np

Writing matrices

The matrix $A=\begin{pmatrix}1&1 \newline 2&-1\end{pmatrix}$ can be written as

a = np.array([[1, 1], [2, -1]])

Try it out

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Interacting with matrices

Here is a reduced list of useful Numpy functions for matrices:

• + and - can be used to add or subtract matrices
• * can be used to multiply all terms within a matrix by a constant
• ** can be used to calculate the exponent of all terms within a matrix by a constant
• np.dot(a,b) calculate dot product of matrices a and b
• np.linalg.inv(m) calculate inverse of matrix m
• np.transpose(m) transpose a matrix m
• np.linalg.det(m) calculates the determinant of a matrix m
• np.shape(m) returns the dimensions of the matrix m

Solving linear equations with matrices

Let’s solve the following simultaneous linear equations with matrices in Python.

$\begin{align} x + y + z &= 7 \newline 2x -y + 2z &= 8 \newline 3x + 2y -z &= 11 \end{align}$

We can write the following code to solve this:

import numpy as np

A = np.array([[1, 1, 1], [2, -1, 2], [3, 2, -1]])
b = np.array([[7], [8], [11]])

x = np.dot(np.linalg.inv(A), b)

Try it out