Eigenvalues and eigenvectors calculator

This calculator allows you to enter any square matrix from 2x2, 3x3, 4x4 all the way up to 9x9 size. It will find the eigenvalues of that matrix, and also outputs the corresponding eigenvectors.

For background on these concepts, see 7. Eigenvalues and Eigenvectors

Instructions

First, choose the matrix size you want to enter. You will see a randomly generated matrix to give you an idea of what your output will look like.

Then, enter your own numbers in the boxes that appear. You can enter integers or decimals. (More advanced entry and output is in the works, but not available yet.)

On a keyboard, you can use the tab key to easily move to the next matrix entry box.

Click calculate when ready.

The output will involve either real and/or complex eigenvalues and eigenvector entries.

You can change the precision (number of significant digits) of the answers, using the pull-down menu.

NOTE 1: The eigenvector output you see here may not be the same as what you obtain on paper. Remember, you can have any scalar multiple of the eigenvector, and it will still be an eigenvector. The convention used here is eigenvectors have been scaled so the final entry is 1.

NOTE 2: The larger matrices involve a lot of calculation, so expect the answer to take a bit longer.

NOTE 3: Eigenvectors are usually column vectors, but the larger ones would take up a lot of vertical space, so they are written horizontally, with a "T" superscript (known as the transpose of the matrix).

NOTE 4: When there are complex eigenvalues, there's always an even number of them, and they always appear as a complex conjugate pair, e.g. 3 + 5i and 3 − 5i.

NOTE 5: When there are eigenvectors with complex elements, there's always an even number of such eigenvectors, and the corresponding elements always appear as complex conjugate pairs. (It may take some manipulating by multiplying each element by a complex number to see this is so in some cases.)

Credit: This calculator was built using the Numeric.js library.