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    Matrix Algebra - Definite vs. Indefinite

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    Let A be an nxn symmetric matrix such that det {see attachment}. We know from the matrix algebra that the associated quadratic form {see attachment}, where x = (x1,...xn), is either positive-definite, negative- definite or indefinite.
    Now assume the diagonal entries of A are all zero. Explain why q(x) is indefinite.
    (Hint: A criterion in terms of the signs of the diagonal minors)

    © BrainMass Inc. brainmass.com February 24, 2021, 2:35 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/matrix-algebra-definite-vs-indefinite-30745

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    Let A be an n x n symmetric matrix such that det (A) 0. We know from the matrix algebra that the associated quadratic form q(x) = , where x = (x1,...xn), is either ...

    Solution Summary

    The definite versus indefinite matrix algebras are found. Diagonal entries being zeros are analyzed.

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