Show how to classify a quadratic form Q(x) = x T Ax, when and det A
Question:
Show how to classify a quadratic form Q(x) = xTAx, when 
and det A ≠ 0, without finding the eigenvalues of A.
If λ1 and λ2 are the eigenvalues of A, then the characteristic of A can be written in two ways: det(A - λI) and (λ – λ) (λ – λ2) Use this fact to show that λ1 + λ2 = a + d (the diagonal entries of A) and λ1λ2 = det A.
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The characteristic polynomial of A m...View the full answer
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Related Book For 
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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