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Martin Sleziak
Martin Sleziak
06:24
@Royi Since you have used @username in your post, I'll mention that greg is not getting a notification from your message in chat. (Since he has not visited this chatroom.) But most likely you know this.
For the sake of better readability, the post linked above is: Gradient of the spectral norm of a matrix
1
Q: Gradient of the spectral norm of a matrix

puloskyLet $X \in \mathbb{R}^{a \times b}$ and $$\|X\|_2 = \sigma_{\max}(X) = \sqrt{\lambda_{\max} \left( X^T X \right)}$$ How can I compute $\nabla_X \|AX\|_2$, where $A \in \mathbb{R}^{c \times a}$ is some known matrix?

linear-algebra derivatives norm matrix-calculus singular-values
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A: Gradient of the spectral norm of a matrix

gregConsider a matrix and its SVD $$Y = \sum_{k=1}^r\sigma_ku_kv_k$$ and let $\,\phi=\|Y\|=\sigma_1\,$ be the spectral norm $($assuming that the singular values are ordered such that $\sigma_1>\sigma_2>\sigma_3>\ldots>\sigma_r>0\,)$ The gradient of the norm is $$\frac{\partial\phi}{\partial Y} = u_...

Royi
Royi
07:24
@MartinSleziak, Thank you. I think the issue is begin not able to calculate the gradient numerically. As in the case I pointed the function is not smooth. But I'd be happy to have more knowledgeable people idea about this.

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