Similar Matrices

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.

References in periodicals archive ?
3] as the one F* - KH* because they are similar matrices.
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.
RM 8504, Transformer Oil, is intended to be used as a diluent oil with transformer oil Standard Reference Materials (SRMs) 3075 to 3080 and SRM 3090 [1] when developing and validating methods for the determination of polychlorinated biphenyls (PCBs) as Aroclors (1) 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.