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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 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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A new reference material (RM), RM 8504, has been prepared for use as a diluent oil with Aroclors in transformer oil Standard Reference Materials (SRMs) 3075 to 3080 and SRM 3090 when developing and validating methods for the determination of polychlorinated biphenyls (PCBs) as Aroclors in transformer oil or similar matrices.
Spatial tests such as Block Design do produce sex-specific results (Jensen 1980), but sex differences are not usually found with Raven's tests or similar matrices tests [see Table 4.
With the CD-MAP, similar matrices are deployed to analyse the needs of internal customers and stakeholders using the same techniques as for external customers.
 
 
 
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