“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	TheInverseImageCommutesWithSetOperations the inverse image commutes with set operations TheJinvariantClassifiesEllipticCurvesUpToIsomorphism the j-invariant classifies elliptic curves up to isomorphism TheKernelOfAGroupHomomorphismIsANormalSubgroup the kernel of a group homomorphism is a normal subgroup TheLimitOfAUniformlyConvergentSequenceOfContinuousFunctionsIsContinuous the limit of a uniformly convergent sequence of continuous functions is continuous The logic of mere propositions TheMultiplicativeIdentityOfACyclicRingMustBeAGenerator the multiplicative identity of a cyclic ring must be a generator The natural numbers The object classifier TheOddBernoulliNumbersAreZero the odd Bernoulli numbers are zero TheOnlyCompactMetricSpacesThatAdmitAPositivelyExpansiveHomeomorphismAreDiscreteSpaces the only compact metric spaces that admit a positively expansive homeomorphism are discrete spaces TheoremAboutContinuousConvergence theorem about continuous convergence TheoremAboutCyclicSubspaces theorem about cyclic subspaces TheoremForNormalMatrices theorem for normal matrices TheoremForNormalTriangularMatrices theorem for normal triangular matrices

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

symmetric matrix