Similar matrices

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Square matrices $A$ and $B$ of the same order related by $B=S^{-1}AS$, where $S$ 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).

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