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Similar Matrices |
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similar matrices [¦sim·i·lər ′mā·tri‚sēz]
(mathematics) Two square matricesAandBrelated by the transformationB=SAT, whereSandTare nonsingular matrices andTis the inverse matrix ofS. 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 λE – Aǀ and ǀλE – Bǀ and, consequently, the determinants ǀA and ǀBǀ and the eigenvalues of the similar matrices A and B coincide. Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content. |
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