Namespaces
Variants
Actions

Difference between revisions of "Similar matrices"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(TeX encoding is done)
Line 1: Line 1:
−
Square matrices <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085110/s0851101.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085110/s0851102.png" /> of the same order related by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085110/s0851103.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085110/s0851104.png" /> 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|Jordan matrix]]).
+
{{TEX|done}}
 +
 
 +
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|Jordan matrix]]).

Revision as of 18:17, 7 December 2012


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).

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
Retrieved from "https://encyclopediaofmath.org/index.php?title=Similar_matrices&oldid=29125"