I am sorry if this is a dumb question. Today I've come across for the first time with the notion of spectral norm of a matrix. I have read that it is the biggest singular value of a matrix.
In the context of SVD, let $X=U \Sigma V^*$
What is the spectral norm of $\Sigma$? Are the singular values of $X$ (contained in $\Sigma$) also the singular values of $\Sigma$?
Yes, the singular values of $X$ are equal to the singular values of $\Sigma$.