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

单词	TheoremAboutCyclicSubspaces
释义	theorem about cyclic subspaces Let $k$ be field, $V$ a vector space over $k$ , $\\dim V=n$ , and $T:V\\to V$ a linear operator. Let $W$ be a subspace of $V$ . And let $v_{1},\\ldots,v_{r}\\in V$ such that $W=Z(v_{1},T)\\bigoplus\\cdots\\bigoplus Z(v_{r},T)$ (see the cyclic subspace definition), and $(m_{v_{i}},m_{v_{j}})=1$ if $i\eq j$ , where $m_{v}$ denotes the minimal polynomial of $v$ (or in other words, its annihilator polynomial). Then, $Z(v_{1}+\\cdots+v_{r},T)=Z(v_{1},T)\\bigoplus\\cdots\\bigoplus Z(v_{r},T)$ , and $m_{v_{1}+\\cdots+v_{r}}=m_{v_{1}}\\cdots m_{v_{r}}$ .
随便看	ExamplesOfPolydivisibleNumbers examples of polydivisible numbers ExamplesOfPrimeIdealDecompositionInNumberFields examples of prime ideal decomposition in number fields ExamplesOfPrimitiveGroupsThatAreNotDoublyTransitive examples of primitive groups that are not doubly transitive ExamplesOfPrimitiveRecursiveEncoding examples of primitive recursive encoding ExamplesOfPrimitiveRecursiveFunctions examples of primitive recursive functions ExamplesOfPrimitiveRecursivePredicates examples of primitive recursive predicates ExamplesOfProbablePrimes examples of probable primes ExamplesOfRadicalsOfIdealsInCommutativeRings examples of radicals of ideals in commutative rings ExamplesOfRamificationOfArchimedeanPlaces examples of ramification of archimedean places ExamplesOfRangesOfConsecutiveIntegersForErdHosWoodsNumbers examples of ranges of consecutive integers for Erdős-Woods numbers ExamplesOfRegularPrimes examples of regular primes ExamplesOfRingOfIntegersOfANumberField examples of ring of integers of a number field ExamplesOfRingOfSets

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。

theorem about cyclic subspaces