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I want a lower bound on the smallest eigenvalue of $AA^T$ in terms of the Frobenius norm of $A$

score 93 · Answer 1 · 2022-08-04 12:16:15

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I want a lower bound on the smallest eigenvalue of $AA^T$ in terms of the Frobenius norm of $A$

Published on 04 Aug 2022 - 12:16

score 121 · Answer 2 · 2026-03-26 01:28:58

121

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score 116 · Answer 3 · 2022-08-24 15:33:16

116

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score 82 · Answer 7 · 2022-11-02 03:15:18

82

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68

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score 144 · Answer 15 · 2023-01-08 12:37:46

144

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List Question

I want a lower bound on the smallest eigenvalue of $AA^T$ in terms of the Frobenius norm of $A$

How to prove ${\lambda _n}\left( {{X^T}AX} \right) \le {\lambda _n}\left( A \right){\rho ^2}\left( X \right)$?

Ratio between min and max value of a quadratic function

Bounds on spectral radius of $2\text{diag}(h)+h \cdot 1^T$

If in a matrix I add rows to each other, does its spectral radius change?

How to find the spectral radius of a compact operator $T$

Why is $\rho(A) = \lim_{n \to \infty}\|A^n\|^{1/n}$ for any matrix norm $\|\cdot\|$?

The largest eigenvalue of a singular random matrix

Terminology problem: what if the historical term is not convenient for me while writing paper?

How to generate square matrices based on constraints on their spectral radii?

Spectral Radius of Perturbed Matrix

Estimate spectral radius of general square matrix

Is the second norm of matrix $A$ equal to its maximum absolute eigenvalue if $A^TA$ is symmetric?

How to calculate the spectral radius of $A^TA$ where the matrix $A$ is not symmetric but has same diagonal elements

minimizing maximum eigenvalue of a matrix

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