# Orthonormal basis consisting of eigenvectors of a matrix

How to find an orthonormal basis consisting of eigenvectors of a matrix. We assume that the matrix is over reals.

Orthonormal basis consisting of eigenvectors of a matrix

asked
**
2015-04-14 04:21:01 -0500
**

This post is a wiki. Anyone with karma >750 is welcome to improve it.

Asked: **
2015-04-14 04:21:01 -0500
**

Seen: **775 times**

Last updated: **Apr 14 '15**

Condensing variables of a matrix

eigenvalues of a derivative vs derivative of eigenvalues

QZ decomposition for generalized eigenvalues

Eigenvalues/vectors of jacobian matrix as complex numbers

How to convert sagemath matrix to R matrix?

Problems in solving eigenvalue equations with differential operators

Why can 'matrix' not use cached functions?

Can I get a exact solution for SVD?

How should I get symbolic expression of eigenvalues and eigenvectors of a real symmetric matrix 3x3

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

The eigenvectors of a matrix do not necessarily form an orthonormal basis. Could you precise your question?

For example, a unitary matrix over the field of reals.

If

`m`

is a matrix, then`m.eigenvectors_left()`

gives its eigenvectors. That should suffice, right?