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In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: The concept of normal matrices can be extended to normal operators on infinite dimensional normed spaces and to normal elements in C*-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C*-algebras, more amenable to analysis.

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rdfs:label	Normal matrix (en)
rdfs:comment	In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A: The concept of normal matrices can be extended to normal operators on infinite dimensional normed spaces and to normal elements in C-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C*-algebras, more amenable to analysis. (en)
sameAs	Normal matrix Normal matrix
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prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Normal_matrix?oldid=1073950518&ns=0
Wikipage page ID	170366 (xsd:integer)
page length (characters) of wiki page	12483 (xsd:nonNegativeInteger)
Wikipage revision ID	1073950518 (xsd:integer)
Link from a Wikipage to another Wikipage	Normal operator Skew-Hermitian matrix Skew-symmetric matrix Unit circle Unitary matrix Self-adjoint C*-algebra Positive real numbers Quasinormal operator Zero matrix Definite matrix Square matrix Triangular matrix Commutative property Commuting matrices Complex conjugate Complex number Conjugate transpose Eigenvalues and eigenvectors Hermitian matrix Normed vector space Ordinary least squares Orthogonal matrix Orthogonality Orthonormal basis Spectral theorem Idempotent matrix Unit matrix Imaginary number Scaling (geometry) Schur decomposition Symmetric matrix Diagonal matrix Diagonalizable matrix Invertible matrix Involutory matrix Matrix norm Matrix similarity Polar decomposition Real number Singular value Singular value decomposition
has abstract	In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A: The concept of normal matrices can be extended to normal operators on infinite dimensional normed spaces and to normal elements in C-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C-algebras, more amenable to analysis. The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A satisfying the equation AA = AA* is diagonalizable. The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces. The left and right singular vectors in the singular value decomposition of a normal matrix differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored out of the eigenvalues to form singular values. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Normal_matrix
is Wikipage redirect of	Normal matrices Normal transformation
is Link from a Wikipage to another Wikipage of	Normal Normal element Normal map Normal matrices Normal operator Numerical range AW*-algebra Adjugate matrix Alternating-direction implicit method Bauer–Fike theorem Moore–Penrose inverse Normal transformation Canonical form Gelfand representation Generalized minimal residual method Jordan normal form Defective matrix Linear algebra List of functional analysis topics List of named matrices Compound matrix Condition number Conjugate transpose Convex hull Eigendecomposition of a matrix Eigenvalue algorithm Hermitian matrix Nick Trefethen Gram matrix Determinantal conjecture Diagonal matrix Diagonalizable matrix Fermat (computer algebra system) Hadamard's maximal determinant problem Involutory matrix Moment matrix Euler's rotation theorem Least-squares adjustment

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