# Jorge Valle

Jorge Valle is a front end developer with a particular passion for, and expertise in, JavaScript and user interfaces. Lately, he's also been diving into machine learning.

# Finding the eigenvalues of a matrix

## Index

Finding the eigenvalues of a matrix can be done by solving the characteristic equation.

## Matrix used

Here's the matrix I will be referring to.

## Solving the characteristic equation

To find the eigenvalues of the above A, we solve the characteristic equation, which is defined as follows.

In this case, $I$ is simply the identity matrix. Swapping in $A$ and $I$ yields the following.

$1$ times $λ$ is just $λ$, so we can clarify further.

Then, we do the simple subtraction.

Remembering how to find the determinant, we can then express this as follows.

This can be rearranged to a tidier expression.

This is now the characteristic polynomial, with solutions at 5 and -1: these are the eigenvalues of $A$.

## Numpy implementation

This is the method for returning eigenvalues in Numpy. Note that the similar numpy.linalg.eig() method returns both the eigenvalues and the eigenvectors.