Negative-definite matrices

In mathematics, a symmetric matrix M with real entries is positive-definite if the real number x^T M x is positive. Negative-definite matrices are defined analogously... Wikipedia: Definite matrix

The eigenvalues ​​of a negative-definite matrix are negative. The matrix is ​​invertible. -A is a positive-definite matrix

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Let's check that A = V * EValue * VT.

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The inverse matrix of a negative-definite matrix is ​​negative definite.

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If A is negative-definite and if s is a strictly positive real number, then s*A is negative definite.

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The code

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