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con·sim·i·lar·i·ty
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- In linear algebra, two n-by-n matrices A and B are called consimilar if A = S B S ¯ − 1 {\displaystyle A=SB{\bar {S}}^{-1}\,} for some invertible n × n {\displaystyle n\times n} matrix S {\displaystyle S} , where S ¯ {\displaystyle {\bar {S}}} denotes the elementwise complex conjugation. So for real matrices similar by some real matrix S {\displaystyle S} , consimilarity is the same as matrix similarity. Like ordinary similarity, consimilarity is an equivalence relation on the set of n × n {\displaystyle n\times n} matrices, and it is reasonable to ask what properties it preserves. The theory of ordinary similarity arises as a result of studying linear transformations referred to different bases. Consimilarity arises as a result of studying antilinear transformations referred to different bases. A matrix is consimilar to itself, its complex conjugate, its transpose and its adjoint matrix. Every matrix is consimilar to a real matrix and to a Hermitian matrix. There is a standard form for the consimilarity class, analogous to the Jordan normal form.
We couldn't find any rhymes for the word consimilarity.
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consiglio, consign, consigned, consignment, consist, consisted, consistence, consistency, consistent
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"consimilarity Rhymes." Rhymes.com. STANDS4 LLC, 2024. Web. 6 May 2024. <https://www.rhymes.com/rhyme/consimilarity>.
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