# Similar Matrices

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## similar matrices

[¦sim·i·lər ′mā·tri‚sēz]
(mathematics)
Two square matrices A and B related by the transformation B = SAT, where S and T are nonsingular matrices and T is the inverse matrix of S.

## Similar Matrices

Two square matrices A and B of order n are said to be similar if there exists a nonsingular, or invertible, matrix P of order n such that B= P-1AP. Similar matrices are obtained when the matrix of a linear transformation is given in different coordinate systems. The role of the matrix P in this case is played by the matrix of the transformation of coordinates. For a given matrix A it is often important to select a second matrix B that is similar to A and has as simple a form as possible—for example, the Jordan matrix. Similar matrices are of identical rank. The characteristic polynomials ǀ λEAǀ and ǀλEBǀ and, consequently, the determinants ǀA and ǀBǀ and the eigenvalues of the similar matrices A and B coincide.

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It's logical to assume all FFIEC members, which include the NCUA, may adopt a similar matrix, he said.
A similar matrix is devised in order to match the user activity log and its pattern in a transformed space.
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A similar matrix for purchasers of RTA furniture at discount stores shows that about one-third (31.
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However, it is possible to develop a similar matrix just as relevant to CPA firms.

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