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In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.

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rdf:type	Thing
rdfs:label	Symmetric matrix (en)
rdfs:comment	In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. (en)
sameAs	Symmetric matrix Symmetric matrix
dbp:wikiPageUsesTemplate	dbt:About dbt:Anchor dbt:Authority_control dbt:Citation dbt:Div_col dbt:Div_col_end dbt:Equation_box_1 dbt:For dbt:Reflist dbt:Relevance_inline dbt:Short_description dbt:Use_American_English dbt:Springer dbt:Matrix_classes
Subject	Matrices
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Symmetric_matrix?oldid=1067795438&ns=0
Wikipage page ID	126474 (xsd:integer)
page length (characters) of wiki page	16822 (xsd:nonNegativeInteger)
Wikipage revision ID	1067795438 (xsd:integer)
has abstract	In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries. Symmetric matrices appear naturally in a variety of applications, and typical numerical linear algebra software makes special accommodations for them. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Symmetric_matrix
is Wikipage redirect of	Autonne-Takagi factorization Symmetric matrices Autonne–Takagi factorization Real symmetric matrix Takagi factorization Complex symmetric matrix Symmetric (matrix) Symmetric array Symmetrizable matrix
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