Symmetric Matrix
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symmetric matrix [sə′me·trik ′mā·triks]

(mathematics)

A matrix which equals its transpose.

Symmetric Matrix

a square matrix S = ||s_ik|| in which any two elements that are symmetrically located with respect to the principal diagonal are equal: s_ik = s_ki, where i, k = 1, 2,…, n. A symmetric matrix is often treated as the matrix of the coefficients of some quadratic form. The theory of symmetric matrices and the theory of quadratic forms are closely related.

The properties of the spectrum of a symmetric matrix with real elements include the following: (1) all the roots λ₁, λ₂,…, λ_n of the characteristic equation of the matrix are real; and (2) to these roots there correspond n pairwise orthogonal eigenvectors of the matrix, where n is the order of the matrix. A symmetric matrix with real elements can always be represented in the form S″ = ODO^-1, where O is an orthogonal matrix and

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No references found			456 QA251 Fourteen papers accepted for the December 2006 conference describe the structure of incidence rings of group automata, apply diagram categories from statistical mechanics to representation theory, and examine determinantal and Pfaffian ideals of symmetric matrices over general commutative rings. Noncommutative rings, group rings, diagram algebras and their ... by SciTech Book News			Syme, Sir Ronald Symeon Symeon Logothetes Symeon Metaphrastes Symeon the New Theologian Symington, Stuart Symington, William Symington, William Stuart symlink Symmachia Symmachus, Quintus Aurelius symmetric symmetric chain symmetric chain decomposition symmetric compression symmetric design symmetric difference symmetric distribution symmetric encryption symmetric form Symmetric Function Symmetric Group symmetric key cryptography Symmetric LISP symmetric list Symmetric matrices Symmetric Matrix symmetric multiprocessing symmetric multiprocessor symmetric relation symmetric ripple mark symmetric space symmetric spherical triangles symmetric tensor symmetric top molecule symmetric transformation symmetrical achromat lens symmetrical alternating quantity symmetrical architecture symmetrical avalanche rectifier symmetrical band-pass filter symmetrical band-reject filter symmetrical clipper symmetrical deflection symmetrical distribution symmetrical fold symmetrical H attenuator symmetrical inductive diaphragm symmetrical lens symmetrical O attenuator symmetrical pi attenuator			Symmetric Dimethylarginine symmetric distribution Symmetric DSL Symmetric DSL Symmetric Eigenproblems Symmetric encryption symmetric form Symmetric function Symmetric Galerkin Boundary Element Method symmetric gangrene symmetric gangrene symmetric gangrene Symmetric Gaussian Distribution symmetric group symmetric group Symmetric Group Graphical Approach Symmetric High-speed Digital Subscriber Line Symmetric Interior Penalty Galerkin Symmetric kernel Symmetric Key Client Library Symmetric key cryptography Symmetric Key Infrastructure Symmetric Key Services Markup Language symmetric lipomatosis Symmetric LISP symmetric list Symmetric List Processor Symmetric Mach-Zehnder Symmetric matrices symmetric matrix symmetric matrix Symmetric Multi Processing Symmetric Multi-Processor Symmetric Multi-Processor Symmetric multiprocessing Symmetric multiprocessing Symmetric multiprocessing Symmetric multiprocessing Symmetric multiprocessor Symmetric NAT symmetric orientation Symmetric Pareto Symmetric Phase Only Filtering Symmetric Phase Shift Keying Symmetric Phase-Only Matched Filter Symmetric power Symmetric Pre-Shared Key Symmetric Private Information Retrieval Symmetric property Symmetric property Symmetric property Symmetric property symmetric quadrature master equation Symmetric Quasi-Minimal Residual Symmetric Rank-K Symmetric relation Symmetric Remote Data Facility Symmetric Remote Data Facility-Data Mobility Symmetric Reversible Variable Length Code

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Symmetric Matrix (redirected from Symmetric matrices)

Symmetric Matrix
(redirected from Symmetric matrices)