 Classroom Tips and Techniques: Simultaneous Diagonalization and the Generalized Eigenvalue Problem - Maple Application Center
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## Classroom Tips and Techniques: Simultaneous Diagonalization and the Generalized Eigenvalue Problem This Application runs in Maple. Don't have Maple? No problem!

This article explores the connections between the generalized eigenvalue problem and the problem of simultaneously diagonalizing a pair of n × n matrices.

Given the n × n matrices A and B, the generalized eigenvalue problem seeks the eigenpairs (lambdak, xk), solutions of the equation Ax = lambda Bx, or (A - lambda B) x = 0. If B is nonsingular, the eigenpairs of B-1 A are solutions. If a matrix S exists for which ST A S = Lambda, and ST B S = I, where Lambda is a diagonal matrix and I is the n × n identity, then A and B are said to be diagonalized simultaneously, in which case the diagonal entries of Lambda are the generalized eigenvalues for A and B. Such a matrix S exists if A is symmetric and B is positive definite. (Our definition of positive definite includes symmetry.)

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Publish Date: December 06, 2011
Created In: Maple 15
Language: English

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