characteristic eigenvalue

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• Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …   Wikipedia

• Eigenvalue algorithm — In linear algebra, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Contents 1 Characteristic polynomial 2 Power… …   Wikipedia

• Characteristic polynomial — This article is about the characteristic polynomial of a matrix. For the characteristic polynomial of a matroid, see Matroid. For that of a graded poset, see Graded poset. In linear algebra, one associates a polynomial to every square matrix: its …   Wikipedia

• eigenvalue — /uy geuhn val yooh/, n. Math. See characteristic root. [1925 30; partial trans. of G Eigenwert, equiv. to eigen characteristic, particular + Wert VALUE] * * * In mathematical analysis, one of a set of discrete values of a parameter, k, in an… …   Universalium

• characteristic root — noun : eigenvalue herein * * * Math. 1. a scalar for which there exists a nonzero vector such that the scalar times the vector equals the value of the vector under a given linear transformation on a vector space. 2. a root of the characteristic… …   Useful english dictionary

• characteristic root of a square matrix — noun (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant • Syn: ↑eigenvalue, ↑eigenvalue of a matrix, ↑eigenvalue of a square matrix • Hypernyms: ↑value …   Useful english dictionary

• eigenvalue of a matrix — noun (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant • Syn: ↑eigenvalue, ↑eigenvalue of a square matrix, ↑characteristic root of a square matrix • Hypernyms: ↑value …   Useful english dictionary

• eigenvalue of a square matrix — noun (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant • Syn: ↑eigenvalue, ↑eigenvalue of a matrix, ↑characteristic root of a square matrix • Hypernyms: ↑value …   Useful english dictionary

• Characteristic multiplier — In mathematics, and particularly ordinary differential equations, a characteristic multiplier is an eigenvalue of a monodromy matrix. The logarithm of a characteristic multiplier is also known as characteristic exponent. They appear in Floquet… …   Wikipedia

• characteristic root — Math. 1. a scalar for which there exists a nonzero vector such that the scalar times the vector equals the value of the vector under a given linear transformation on a vector space. 2. a root of the characteristic equation of a given matrix. Also …   Universalium

• eigenvalue — noun /ˈaɪɡənˌvæljuː/ The change in magnitude of a vector that does not change in direction under a given linear transformation; a scalar factor by which an eigenvector is multiplied under such a transformation. The eigenvalues of a transformation …   Wiktionary