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单词 Eigenvalue1
释义

eigenvalue


Let V be a vector spaceMathworldPlanetmath over k and T a linear operatorMathworldPlanetmath on V.An eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath for T is an scalar λ (that is, an element of k) such thatT(z)=λz for some nonzero vector zV.Is that case, we also say that z is an eigenvectorMathworldPlanetmathPlanetmathPlanetmath of T.

This can also be expressed as follows: λ is an eigenvalue for T if the kernel of A-λI is non trivial.

A linear operator can have several eigenvalues (but no more than the dimensionPlanetmathPlanetmath of the space). Eigenvectors corresponding to different eigenvalues are linearly independentMathworldPlanetmath.

Titleeigenvalue
Canonical nameEigenvalue1
Date of creation2013-03-22 14:01:53
Last modified on2013-03-22 14:01:53
Ownerdrini (3)
Last modified bydrini (3)
Numerical id8
Authordrini (3)
Entry typeDefinition
Classificationmsc 15A18
Related topicLinearTransformation
Related topicScalar
Related topicVector
Related topicKernel
Related topicDimension2
Defineseigenvector
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更新时间:2025/5/4 17:57:59