About: Reducing subspace

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In linear algebra, a reducing subspace of a linear map from a Hilbert space to itself is an invariant subspace of whose orthogonal complement is also an invariant subspace of That is, and One says that the subspace reduces the map One says that a linear map is reducible if it has a nontrivial reducing subspace. Otherwise one says it is irreducible. If is of finite dimension and is a reducing subspace of the map represented under basis by matrix then can be expressed as the sum with where , and

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rdfs:label	Reducing subspace (en)
rdfs:comment	In linear algebra, a reducing subspace of a linear map from a Hilbert space to itself is an invariant subspace of whose orthogonal complement is also an invariant subspace of That is, and One says that the subspace reduces the map One says that a linear map is reducible if it has a nontrivial reducing subspace. Otherwise one says it is irreducible. If is of finite dimension and is a reducing subspace of the map represented under basis by matrix then can be expressed as the sum with where , and (en)
dcterms:subject	Matrices Linear algebra
Wikipage page ID	69116423 (xsd:integer)
Wikipage revision ID	1053967677 (xsd:integer)
Link from a Wikipage to another Wikipage	Basis (linear algebra) Invariant subspace Linear algebra Identity matrix Orthonormal basis Matrices Linear map Linear subspace Linear algebra Dimension (vector space) Hilbert space Change of basis Orthogonal complement Orthogonal projection Block-diagonal matrix
sameAs	Reducing subspace Reducing subspace
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Linear-algebra-stub
has abstract	In linear algebra, a reducing subspace of a linear map from a Hilbert space to itself is an invariant subspace of whose orthogonal complement is also an invariant subspace of That is, and One says that the subspace reduces the map One says that a linear map is reducible if it has a nontrivial reducing subspace. Otherwise one says it is irreducible. If is of finite dimension and is a reducing subspace of the map represented under basis by matrix then can be expressed as the sum where is the matrix of the orthogonal projection from to and is the matrix of the projection onto (Here is the identity matrix.) Furthermore, has an orthonormal basis with a subset that is an orthonormal basis of . If is the transition matrix from to then with respect to the matrix representing is a block-diagonal matrix with where , and (en)
prov:wasDerivedFrom	wikipedia-en:Reducing_subspace?oldid=1053967677&ns=0
page length (characters) of wiki page	2237 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Reducing_subspace
is Link from a Wikipage to another Wikipage of	Quasinormal operator Contraction (operator theory) Sufficient dimension reduction Subnormal operator Outline of linear algebra
is foaf:primaryTopic of	wikipedia-en:Reducing_subspace

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