# Similar matrices

From Encyclopedia of Mathematics

Square matrices and of the same order related by , where is a non-degenerate matrix of the same order. Similar matrices have the same rank, the same determinant, the same characteristic polynomial, and the same eigenvalues. It is often important to select a matrix similar to a given one but having a possibly simpler form, for example, a diagonal or Jordan form (see Jordan matrix).

**How to Cite This Entry:**

Similar matrices.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Similar_matrices&oldid=12846

This article was adapted from an original article by T.S. Pigolkina (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article