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16 Questions

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If an eigenvalue of an integer matrix lies on the unit circle, must it be a root of unity?

Oct 13 '19 at 4:06 user1551 108k

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If $A^T A v = A A^T v = v$ with $A$ not orthogonal. Must $v$ be an eigenvector?

linear-algebra eigenvalues-eigenvectors

Jul 2 at 14:44 lhl73 251

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Approximating $\sum_i \frac{a_i}{\lambda - \lambda_i} = \lambda$

real-analysis linear-algebra systems-of-equations

Apr 16 '19 at 5:26 Claude Leibovici 182k

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Must all unitary eigenvalues be non-defective?

linear-algebra matrices eigenvalues-eigenvectors

Jul 29 at 15:48 Leo 589

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Significance of the length of the Perron eigenvector

matrices eigenvalues-eigenvectors spectral-theory

Feb 17 '20 at 16:30 Leo 589

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answer

124

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Matrix and its inverse have the same singular values

linear-algebra matrices singular-values

Nov 24 '19 at 17:49 Robert Israel 400k

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Number of real eigenvalues of a matrix function with constant rank.

linear-algebra matrices eigenvalues-eigenvectors matrix-rank

Oct 19 '19 at 19:47 Arthur 174k

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When does this complex symmetric matrix have a real eigenvalue?

linear-algebra complex-numbers eigenvalues-eigenvectors symmetric-matrices

Oct 19 '19 at 18:52 Leo 589

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If a real matrix has a complex eigenvalue on the unit circle, when is it a root of unity?

complex-numbers eigenvalues-eigenvectors roots-of-unity

Oct 14 '19 at 17:27 Will Jagy 123k

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Support of a generalized eigenvector

linear-algebra matrices eigenvalues-eigenvectors generalized-eigenvector

Aug 13 at 12:01 Ben Grossmann 182k

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Are there any channels or streams for real-time research mathematics?

soft-question

Mar 7 '20 at 3:43 Leo 589

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Significance of the normalization of the left Perron eigenvector

linear-algebra eigenvalues-eigenvectors spectral-theory

Feb 7 '20 at 22:33 Leo 589

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Smallest singular value is the reciprocal of the largest singular value?

linear-algebra matrix-decomposition singular-values

Nov 21 '19 at 4:46 Leo 589

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Eigenvalues of matrix with large diagonal element

linear-algebra complex-numbers eigenvalues-eigenvectors symmetric-matrices

Oct 13 '19 at 2:54 Kim Juno 186

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How to generalize a property of polynomials to a property of analytic functions?

linear-algebra polynomials analytic-functions

Sep 15 '19 at 0:19 Kavi Rama Murthy 247k

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103

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Generalization of Gram-Schmidt to bilinear forms that are not inner products

linear-algebra linear-transformations inner-products gram-schmidt

Jul 5 '19 at 15:22 cdipaolo 1,066

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16 Questions

If an eigenvalue of an integer matrix lies on the unit circle, must it be a root of unity?

If $A^T A v = A A^T v = v$ with $A$ not orthogonal. Must $v$ be an eigenvector?

Approximating $\sum_i \frac{a_i}{\lambda - \lambda_i} = \lambda$

Must all unitary eigenvalues be non-defective?

Significance of the length of the Perron eigenvector

Matrix and its inverse have the same singular values

Number of real eigenvalues of a matrix function with constant rank.

When does this complex symmetric matrix have a real eigenvalue?

If a real matrix has a complex eigenvalue on the unit circle, when is it a root of unity?

Support of a generalized eigenvector

Are there any channels or streams for real-time research mathematics?

Significance of the normalization of the left Perron eigenvector

Smallest singular value is the reciprocal of the largest singular value?

Eigenvalues of matrix with large diagonal element

How to generalize a property of polynomials to a property of analytic functions?

Generalization of Gram-Schmidt to bilinear forms that are not inner products