A necessary and sufficient condition for positive definiteness of a quadratic form Q(x) = x T Ax

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A necessary and sufficient condition for positive definiteness of a quadratic form Q(x) = x^TAx with symmetric matrix A is that all the principal minors are positive that is,

Show that the form in Prob. 22 is positive definite, whereas that in Prob. 23 is indefinite.

Data from Prob. 22

4x₁² + 12x₁x₂ + 13x₂² = 16

Data from Prob. 23

-11x₁² + 84x₁x₂ + 24x₂² = 156

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Related Book For answer-question

Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

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Question Posted: Oct 03, 2022 07:53 AM

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A necessary and sufficient condition for positive definiteness of a quadratic form Q(x) = x T Ax

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ANSWER To determine if a quadratic form Qx xTAx is positive definite we need to check whether all th...View the full answer

Advanced Engineering Mathematics

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