Matrix derivative with respect to an orthogonal matrix

Asked Nov 04 '16 at 15:40

Active Nov 04 '16 at 15:53

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Consider the following function:

$$\ f(U)= UU^TXUU^TY $$

where $\ U \in \Re^{n*m} $ ,$\ U^TU = I_m$ and X and Y are Symmetric positive definite matrices with dimension $\ n$.

What is the derivative of $\ f(U)$ with respect to $\ U$ ?

Thank you so much

edited Nov 04 '16 at 15:53

asked Nov 04 '16 at 15:40

alireza

@Fimpellizieri what I guess is: $\ 4YUU^TXU $ – alireza Nov 04 '16 at 16:38
How could the derivative of a function from $\mathbb R^{m\times n}$ into $\mathbb R^{n\times n}$ be a $n\times m$ matrix? (Apart from the trivial case $n=1$) – user251257 Nov 04 '16 at 17:00

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