Let A be a symmetric matrix (that is, A AT) with distinct eigenvalues Icirc raquo 1 and Icirc raquo 2 For such a matrix, if v1 and v2 are eigenvectors belonging to the distinct eigenvalues Icirc raquo 1 and Icirc raquo 2, respectively, then v1 and v2 are orthogonal (a) Illustrate this for (b) Prove fact for an n Atilde n symmetric matrix Use the fact that v1 v2 v1Tv2 (as a matrix product) 4 2

Question: Let A be a symmetric matrix (that is, A = AT) with distinct eigenvalues Î»1 and Î»2. For such a matrix, if v1 and v2

Let A be a symmetric matrix (that is, A = AT) with distinct eigenvalues Î»1 and Î»2. For such a matrix, if v1 and v2 are eigenvectors belonging to the distinct eigenvalues Î»1 and Î»2, respectively, then v1 and v2 are orthogonal
(a) Illustrate this for

(b) Prove fact for an n Ã— n symmetric matrix. Use the fact that v1. v2 = v1Tv2 (as a matrix product).

4 2

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