# Questions tagged [singular-values]

This tag is for questions relating to 'Singular Value'. The term “singular value” relates to the distance between a matrix and the set of singular matrices

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### Bound for singular values in terms of traces: a 6th power inequality

In the recent paper of Guth and Maynard on large values of Dirichlet polynomials https://arxiv.org/html/2405.20552v1 there is a linear algebra lemma 4.2. Bound for singular values in terms of traces: ...
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### Numerical Least squares estimation on the norm of the minimiser

I was looking at Proposition 3.2. in Applied Numerical Linear Algebra by JW Demmel, that states that when solving $$\min \|Ax - b\|_2$$ if in the singular value decomposition $\sigma_{min}>0$ then ...
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### What are proper numerical methods to solve IVP at irregular singular point?

I have searched for numerical methods to solve IVP with irregular singular points but didn't find any. What is a proper method I can use to solve such equations? For example, we could consider the ...
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### $l_4$-norm of singular values of random matrix

Let $A$ be an $n \times d$ matrix ($n > d$) with iid standard Gaussian entries. Let $\lambda_1 \ge \lambda_2 \ge \dotsm \lambda_d > 0$ be the non-zero singular values of $A$. What is known about ...
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### Deriving the SVD from the eigendecomposition

If $A$ is a rectangular matrix of dimensions $m\times n$, then $S_L=AA^T$ and $S_R=A^TA$ are square symmetric matrices. Hence, using the eigendecompostion we can write $$S_L=AA^T=U\Lambda_{S_L} U^T$$...
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