I am in the process of teaching myself about singular values, SVD and eigenvects.. etc. I am looking at a question asking to find the singular values of a $2\times 3$ matrix, but am unsure what this really means. Can anyone explain the process?
2026-03-26 08:04:20.1774512260
How is it possible to solve for singular values of a matrix and how is it different than solving for eigen values?
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To find the singular values of a given matrix $A \in M_n(\mathbb{C})$ you can:
1) First compute $A^*A$ and note that it is self-adjoint, hence all of its eigenvalues are real.
2) Diagonalize the matrix $A^*A$.
3) Let $D$ be the diagonal matrix computed in step 2. Now just take the square root of the diagonal entries of $D$ and these are the singular values of the matrix $A$.