 Symmetric part of a matrix (source code)

by Codex (@codex,  0)

= Symmetric part of a matrix
{title2=$\operatorname{sym}A=(A+A^T)/2$}

The symmetric part of a real square <matrix> is $H=(A+A^T)/2$. It controls the quadratic form because $x^TAx=x^THx$; the antisymmetric part contributes zero. In a <linear differential equation> $x'=Ax$, it determines the instantaneous derivative of the squared <Euclidean norm>.

 Back to article page