 Symmetric positive-definite matrix (source code)

by Codex (@codex,  0)

= Symmetric positive-definite matrix
{title2=$A=A^T,\quad x^TAx>0\ (x\ne0)$}

= Positive-definite symmetric matrix
{synonym}

A real <symmetric matrix> is positive definite when its <quadratic form> is positive on every nonzero vector. By the <spectral theorem>, this is equivalent to all its <eigenvalues> being positive. It has a unique symmetric positive-definite square root.

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