“SymmetricMatrix”的概念、定义、习题解题方法及翻译-数学辞典

单词	SymmetricMatrix
释义	symmetric matrix Definition: Let $A=(a_{ij})$ be a square matrix oforder $n$ . The matrix $A$ is symmetric if $a_{ij}=a_{ji}$ for all $1\\leq i\\leq n,1\\leq j\\leq n$ . $A=\\begin{pmatrix}a_{11}&\\cdots&a_{1n}\\\\\\vdots&\\ddots&\\vdots\\\\a_{n1}&\\cdots&a_{nn}\\end{pmatrix}$ Properties: 1. $A^{t}=A$ where $A^{t}$ is the matrix transpose Examples: • $\\begin{pmatrix}a&b\\\\b&c\\end{pmatrix}$ • $\\begin{pmatrix}a&b&c\\\\b&d&e\\\\c&e&f\\end{pmatrix}$
随便看	ProofOfRieszRepresentationTheorem proof of Riesz representation theorem ProofOfRieszRepresentationTheoremForSeparableHilbertSpaces proof of Riesz representation theorem for separable Hilbert spaces proof of Riesz’ Lemma ProofOfRodriguesRotationFormula proof of Rodrigues’ rotation formula ProofOfRollesTheorem proof of Rolle’s theorem ProofOfRouchesTheorem proof of Rouché’s theorem ProofOfRuffasFormulaForContinuousFunctions proof of Ruffa’s formula for continuous functions ProofOfSamplingTheorem proof of sampling theorem ProofOfSchauderFixedPointTheorem proof of Schauder fixed point theorem ProofOfSchroederBernsteinTheoremUsingTarskiKnasterTheorem proof of Schroeder-Bernstein theorem using Tarski-Knaster theorem ProofOfSchursInequality proof of Schur’s inequality ProofOfSchwarzLemma proof of Schwarz lemma ProofOfScottWiegoldConjecture proof of Scott-Wiegold conjecture

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symmetric matrix