Matrix similarity

In linear algebra, two n-by-n matrices A and B are called similar if

for some invertible n-by-n matrix P. Similar matrices represent the same linear operator under two different bases, with P being the change of basis matrix.

A transformation $A\mapsto P^{-1} A P$ is called a similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that P be chosen to lie in H.

单词	Similar transformation
释义	Similar transformation 英语百科 Matrix similarity In linear algebra, two n-by-n matrices A and B are called similar if for some invertible n-by-n matrix P. Similar matrices represent the same linear operator under two different bases, with P being the change of basis matrix. A transformation $A\mapsto P^{-1} A P$ is called a similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that P be chosen to lie in H.
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Similar transformation

Matrix similarity