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

单词	EigenvaluesOfNormalOperators
释义	eigenvalues of normal operators Let $H$ be a Hilbert space and $B(H)$ the algebra of bounded operators in $H$ . Suppose $T\\in B(H)$ is a normal operator. Then 1. - If $\\lambda\\in\\mathbb{C}$ is an eigenvalue of $T$ , then $\\overline{\\lambda}$ is an eigenvalue of $T^{*}$ (the adjoint operator of $T$ ) for the same eigenvector. 2. - Eigenvectors of $T$ associated with distinct eigenvalues are orthogonal. Remark - It is known that for any linear operator eigenvectors associated with distinct eigenvalues are linearly independent. 2 strengthens this result for normal operators.
随便看	classical Stokes’ theorem Classical vs. intuitionistic logic Classical well-orderings ClassificationOfComplexNumbers classification of complex numbers ClassificationOfCoveringSpaces classification of covering spaces ClassificationOfFinitedimensionalRepresentationsOfSemisimpleLieAlgebras classification of finite-dimensional representations of semi-simple Lie algebras ClassificationOfHilbertSpaces classification of Hilbert spaces ClassificationOfIndecomposableRootSystems classification of indecomposable root systems ClassificationOfPlatonicSolids classification of Platonic solids ClassificationOfSemisimpleGroups classification of semisimple groups ClassificationOfSeparableHilbertSpaces classification of separable Hilbert spaces ClassificationOfTopologicalPropertiesAccordingToBehaviourUnderMapping classification of topological properties according to behaviour under mapping ClassNumberDivisibilityInCyclicExtensions class number divisibility in cyclic extensions ClassNumberDivisibilityInExtensions class number divisibility in extensions

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。

eigenvalues of normal operators