Suppose I have a vector field $F(x)=Ax$ where $A$ is a matrix. How can I express $Sx$ without $A$ (use $F$ instead)? Here $S=\dfrac{A+A^T}2$ is symmetric part of $A$.
2026-04-12 07:32:41.1775979161
Question on matrix
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You could express $A$ in terms of $F$ by noting that $$ A = \begin{bmatrix}F(e_1)& \cdots & F(e_n)\end{bmatrix} $$ Where $e_1,\dots,e_n$ is the standard basis. From there, you can apply the formula for $S$.