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Statements

Subject Item

dbr:Matrix_consimilarity

rdf:type

yago:Abstraction100002137 yago:Matrix108267640 yago:Group100031264 yago:Arrangement107938773 yago:Array107939382 yago:WikicatMatrices

rdfs:label

Matrix consimilarity

rdfs:comment

In linear algebra, two n-by-n matrices A and B are called consimilar if for some invertible matrix , where denotes the elementwise complex conjugation. So for real matrices similar by some real matrix , consimilarity is the same as matrix similarity. Like ordinary similarity, consimilarity is an equivalence relation on the set of matrices, and it is reasonable to ask what properties it preserves.

dcterms:subject

dbc:Matrices

dbo:wikiPageID

25981480

dbo:wikiPageRevisionID

974861850

dbo:wikiPageWikiLink

dbr:Equivalence_relation dbr:Matrix_similarity dbr:Matrix_(mathematics) dbr:Adjoint_matrix dbr:Jordan_normal_form dbr:Linear_transformation dbr:Hermitian_matrix dbr:Linear_algebra dbr:Complex_conjugation dbr:Cambridge_University_Press dbr:Antilinear_map dbc:Matrices dbr:Transpose

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dbo:abstract

In linear algebra, two n-by-n matrices A and B are called consimilar if for some invertible matrix , where denotes the elementwise complex conjugation. So for real matrices similar by some real matrix , consimilarity is the same as matrix similarity. Like ordinary similarity, consimilarity is an equivalence relation on the set of 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.

prov:wasDerivedFrom

wikipedia-en:Matrix_consimilarity?oldid=974861850&ns=0

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1731

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wikipedia-en:Matrix_consimilarity