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

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A complex number, ?, that satisfies the equation Ax = ?x, where A is an n × n matrix and x is some vector. In this case, x is called an eigenvector.

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An eigenvalue or characteristic root of a square matrix A is a scalar L that satisfies the equation: det [ A - LI ] = 0 where 'det' is the operator that takes a determinant of its argument, and I is the identity matrix with the same dimensions as A. Contexts: linear algebra

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Eigenvalues, also called the characteristic roots: There is one eigenvalue for each discriminant function. The ratio of the eigenvalues indicates the relative discriminating power of the discriminant functions....

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one of a set of discrete values of a parameter, k, in an equation of the form P = k, in which P is a linear operator (that is, a symbol denoting a ...

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Possible values for a parameter of an equation for which the solutions will be compatible with the boundary conditions.In quantum mechanics the energy eigenvalues for the Schrödinger equation are the possible energy levels for the system.

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The change in length that occurs when the corresponding eigenvector is multiplied by its matrix.

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Type: Term Pronunciation: ī′gĕn-val-yū Definitions: 1. Any of the possible values for a parameter of an equation for which the solution will be compatible with the boundary conditions.

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