**3**

votes

**2**answers

429 views

### S-matrix conjecture: status?

Is the $S$-matrix conjecture still open? I mean the one listed as Problem 7 in this survey.

**1**

vote

**1**answer

183 views

### name for a matrix operation

If $A$ is a matrix and $D$ is a diagonal matrix, is there some special name for $DAD$?

**3**

votes

**2**answers

538 views

### matrices whose entries sum to zero

Let $A$ be a non-singular matrix and let $s(A)$ be the sum of its entries. Under which conditions can it be assured that $s(A) \neq 0$?
if you like, you can assume that $A$ is symmetric.
Here is an ...

**0**

votes

**1**answer

184 views

### eigenvector update formula

Suppose that $B$ is a Hermitian matrix with one known eigenpair $(\lambda,v)$. (assume its the smallest or largest pair, if you like). Form the rank one update $B+\rho bb^{T}$.
Now I'm interested in ...

**2**

votes

**3**answers

225 views

### 'Condition number' for Rayleigh-Ritz quotient

Suppose that $A$ is a Hermitian matrix and that $u,v$ are two vectors. Is there some known function $\kappa(A)$ so that $||u-v|| \leq \kappa(A) |\frac{u^{\*}Au}{u^{\*}u}-\frac{v^{\*}Av}{v^{\*}v}|$?
...

**5**

votes

**2**answers

703 views

### A question about matrices with more details

Let $A,B\in\mathbb{R}^{n\times n}$. Suppose that $B$ is nonsingular and that there exists $m$ reals pairwise distinct $\lambda_{1},\cdots,\lambda_{r},\cdots,\lambda_{m}$ such that
...

**2**

votes

**1**answer

189 views

### Simultaneous decomposition of three projectors

A projector $P$ is a Hermitian matrix satisfying $P^2=P$. For any two projectors, it is easy to show that there exists a unitary matrix $U$ such that both $U^*PU$ and $U^*QU$ are block-diagonal ...

**5**

votes

**0**answers

240 views

### concentration for eigenvectors

I am interested in bounding from above the ratio between the maximum and minimum entries of a Perron vector. The only results that I found in the literature are from the classic masters (Ostrowski and ...

**1**

vote

**4**answers

308 views

### inverse-closed matrix spaces

Is there a known characterization of such spaces?
An example: the space of $n \times n$ matrices spanned by $I$ and $J$ (the identity and all-ones matrices, respectively) is inverse closed by the ...

**1**

vote

**2**answers

212 views

### small sums of entries in submatrices - strange phenomenon

Suppose that $x \in \mathbb{R}^{n}$ is a vector of small positive fractions, i.e. $x_{i} \approx \frac{1}{n}$. The exact values are unknown. I form the matrix $M=diag(x)-\frac{xx^{T}}{2}$ which is a ...

**13**

votes

**2**answers

1k views

### Minimum off-diagonal elements of a matrix with fixed eigenvalues

Hello,
I am en engineer working in radar research. I came accross a problem I cannot seem to find math literature on it.
I can ask it in two different ways. Perhaps depending on the reader, the ...