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Exercise 9

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Suppose that AA is a noninvertible, symmetric 3×33\times3 matrix having eigenvectors v1=[2−12],v2=[141]\vvec_1 = \threevec2{-1}2,\hspace{24pt} \vvec_2 = \threevec141 and associated eigenvalues λ1=20\lambda_1 = 20 and λ2=−4\lambda_2 = -4. Find matrices QQ and DD such that A=QDQTA = QDQ^T.

Austin, Understanding Linear Algebra, §7.1 Symmetric matrices and variance, Exercise 9

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.