I used to think that spectral decomposition is possible if the matrix is Hermitian ( in complex field). And Singular value decomposition is for any matrix. Am I right? I have been reading some other posts but getting more and more confused.
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1Does this answer your question? Intuitively, what is the difference between Eigendecomposition and Singular Value Decomposition? – Anurag A Jun 20 '23 at 19:12
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1In addition to the remark of Anurag A, there are easy trick to get the SVD for positive definite and semidefinite matrices, and even for any symmetric matrices. Hermitian matrices for complex case, too. See, for example Section 39.2. "SVD and the other decompositions" here: https://www.researchgate.net/publication/318066716_Linear_Algebra_Theory_and_Algorithms In particular, Example 39.5 and Example 39.6. – V. Mikaelian Jul 02 '23 at 18:37