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user8675309
  • Member for 4 years, 4 months
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11 votes

How to prove that every orthogonal matrix has determinant $\pm1$ using limits (Strang 5.1.8)?

10 votes
Accepted

Determinant of $A+A^T$ is an odd integer if $\text{det}(A-A^T)=1$.

8 votes
Accepted

Fuglede's theorem in finite-dimensional vector space

7 votes
Accepted

Is any symmetric matrix of which its diagonalvector equals its eigenvalues a diagonal matrix?

7 votes
Accepted

How to maximize $\det(W^*DW)$, where $D$ is real diagonal?

7 votes
Accepted

$A$ is positive semidefinite $\iff \text{det} (B_K) \geq 0$

7 votes
Accepted

How is the rank of a matrix affected by centering the columns of a matrix?

6 votes
Accepted

Construction of QR decomposition for a singular matrix

6 votes
Accepted

challenging inequality with complex numbers

5 votes
Accepted

Is $I-JR$ invertible if $J$ is skew-symmetric and $R$ is symmetric positive semi-definite?

5 votes
Accepted

Computation of Cholesky decomposition of Gram matrix from its components

5 votes
Accepted

$AB=BA$ from $e^{A+B} = e^A e^B$, given Hermitian matrices

5 votes
Accepted

commutes with a nilpotent matrix and invertible

5 votes
Accepted

Gershgorin theorem and strictly diagonally dominant matrix

5 votes
Accepted

find bound on condition number of matrix given matrix norm

5 votes
Accepted

Can an Perron eigenvector of a non-symmetric irreducible nonnegative matrix be also a Perron eigenvector of its transpose?

5 votes
Accepted

Evaluating $\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^{N} \frac{1}{n}$

4 votes

Existence of a negative eigenvalues for a certain symmetric matrix

4 votes
Accepted

The permutation matrices are the doubly stochastic matrices with the highest Frobenius norm

4 votes
Accepted

Trace of product of many matrices related by unitary rotation

4 votes
Accepted

Counterexamples of Matrices

4 votes

Finding Characteristic of a field , order of elements in Subgroup, Centre of Group

4 votes
Accepted

Help with arguing against symmetry proofs.

4 votes

Absoute sum of diagonal elements no more than absolute sum of eigenvalues

4 votes
Accepted

Proof of Matrix Norm Inequality (Hadamard product)

4 votes
Accepted

Frobenius norm and operator norm inequality

4 votes
Accepted

Two random variables not gaussian but whose sum is gaussian

4 votes
Accepted

Prove that $B$ is normal

4 votes

Let $A, B \in M_{n}(\mathbb{C})$. Suppose that all of the eigenvalues of $A$ and $B$ are positive real numbers. If $A^{4}=B^{4}$, prove that $A=B$.

3 votes

Schatten norms Triangle inequality

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