List questions from matrix-analysis

Published on 29 Apr 2026 - 12:25

67

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Does there always exist matrix $X \in M_{m \times r}(\mathbb R)$ such that $AXB$ is in upper/lower triangular form?

Published on 15 Apr 2026 - 6:59

66

Views

Square root of a specific matrix in M(3,Z) over Z

Published on 11 Apr 2026 - 14:56

80

Views

Square root of a specific matrix over $\Bbb Z$

Published on 29 Apr 2026 - 12:25

41

Views

$3 \times 3$ Diagonal matrix as the square of an $3 \times 3$ non diagonal matrix

Published on 13 Apr 2026 - 20:47

280

Views

Is the function $A \mapsto \sum\limits_{j=0}^{\infty} \langle A^j v, A^j v \rangle$ differentiable everywhere?

Published on 13 Apr 2026 - 16:03

1k

Views

Show some eigenvalue properties for $A=xy^*$

Published on 16 Apr 2026 - 14:59

51

Views

There exists $H$ such $S=XH^t+HX^t$ for every simetric $S$

Published on 15 Apr 2026 - 7:57

184

Views

Show: $\sum_{i,j=1}^n |a_{ij}|^2=trA^*A=\sum^n_{i=1}\sigma_i^2$

Published on 13 Apr 2026 - 18:39

86

Views

Suppose a square matrix $A$ has spectral radius $\rho(A) < 1$. Fixing the last row and scaling other entries by $r \in (0,1)$, will $\rho(A)<1$?

Published on 25 Mar 2026 - 9:29

924

Views

Infinite Matrix Multiplication

Published on 15 Apr 2026 - 20:20

791

Views

How do the eigenvalues change if we change the diagonal entries of the matrix?

Published on 01 May 2026 - 5:00

85

Views

Eigendecomposition of $(a^\top X a)X - Xaa^\top X$

Published on 15 Apr 2026 - 9:51

187

Views

How do eigenvalues change if we perturbe the diagonal entries of a matrix?

Published on 01 May 2026 - 15:12

266

Views

How to find Inverse-squared of a matrix

Published on 14 Apr 2026 - 4:13

List Question

Square root and similarity between integer matrices

Does there always exist matrix $X \in M_{m \times r}(\mathbb R)$ such that $AXB$ is in upper/lower triangular form?

Square root of a specific matrix in M(3,Z) over Z

Square root of a specific matrix over $\Bbb Z$

$3 \times 3$ Diagonal matrix as the square of an $3 \times 3$ non diagonal matrix

Is the function $A \mapsto \sum\limits_{j=0}^{\infty} \langle A^j v, A^j v \rangle$ differentiable everywhere?

Show some eigenvalue properties for $A=xy^*$

There exists $H$ such $S=XH^t+HX^t$ for every simetric $S$

Show: $\sum_{i,j=1}^n |a_{ij}|^2=trA^*A=\sum^n_{i=1}\sigma_i^2$

Suppose a square matrix $A$ has spectral radius $\rho(A) < 1$. Fixing the last row and scaling other entries by $r \in (0,1)$, will $\rho(A)<1$?

Infinite Matrix Multiplication

How do the eigenvalues change if we change the diagonal entries of the matrix?

Eigendecomposition of $(a^\top X a)X - Xaa^\top X$

How do eigenvalues change if we perturbe the diagonal entries of a matrix?

How to find Inverse-squared of a matrix

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