# 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)

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

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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 ...

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