Given a matrix $A$, its singular values are denoted as $\sigma_1,\sigma_2,\cdots,\sigma_n$. Since in most of the case, the biggest singular value is much larger than others, I just want to know whether there are some bounds to depict such relation. For example, I want to find something like $$\sum_{i=1}^n\sigma_i\le H\sigma_1$$ Is there any $H$ that we can use?
2026-03-25 17:43:53.1774460633
relation between biggest singular value and the sum of all singular values
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