Linear algebra proves that the eigenvectors A1 and A2 corresponding to different eigenvalues of real symmetric matrix a must be orthogonal

Linear algebra proves that the eigenvectors A1 and A2 corresponding to different eigenvalues of real symmetric matrix a must be orthogonal

First, we prove that: if a is a symmetric matrix of order n, and a and B are n-dimensional column vectors, then = (denotes inner product) (if you study higher generation, then the proposition is obviously true. Because of the symmetric transformation, we need to set up a space a little more, so we don't need to prove it in the way of higher generation.)

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