let A be a p by n matrix.
I am stuck with finding the derivative below as part of my matrix calculations and need help with it please:
$$\frac{d}{dA}tr(AA^T)$$
2026-03-27 22:31:08.1774650668
derivative of trace of product of a matrix by its transpose
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The matrix cookbook is an excellent resource for this sort of problem. In 2.5 it says $$\frac{\partial \mathrm{Tr}[F(A)]}{\partial A}=f(A)^T,$$ where $\partial F(x)/\partial x = f(x)$ holds for scalar $x$.
The cookbook continues from this fact and directly addresses your question in (115), which states $$\frac{\partial \mathrm{Tr}(A^T A)}{\partial A}=\frac{\partial \mathrm{Tr}( AA^T)}{\partial A}=2A.$$