# Tagged Questions

**-3**

votes

**0**answers

59 views

### In what sense could “Maximizing a matrix” be and why? [closed]

So if we have the problem to maximize (or minimize) a matrix. What are the most relevant things to look at ?
Positive Semi-definiteness, the usual classical matrix norms ?
What are the difference ...

**2**

votes

**1**answer

77 views

### Approximation with a rank-$1$ matrix

Given a matrix $A$ (generally speaking, complex and non-square), I want to find an identically-sized matrix $D$ with ${\rm rk} D\le 1$ to minimize the induced operator norm $\|A-D\|_2$. From the ...

**6**

votes

**2**answers

304 views

### $\|T\|_2 \le \sqrt{\|T\|_1\|T\|_\infty}$

Let $T$ be a linear operator acting on a finite-dimensional real or complex
vector space. As a direct consequence (or rather a particular case) of the
Riesz-Thorin theorem, we have
$$ \|T\|_2 \le ...

**10**

votes

**1**answer

280 views

### Hölder's inequality for matrices

I was wondering if the HÃ¶lder's inequality was true for matrix induced norms, i.e. if
$$\|AB\|_1 \leq \|A\|_p\|B\|_q, \quad\forall p,q \in [1,\infty] \text{ s.t. } \tfrac{1}{p}+\tfrac{1}{q} = 1.$$
But ...

**0**

votes

**2**answers

142 views

### Matrix-Norm aquivalence with p-Norm [closed]

Let $A$ be a square Matrix and $||\cdot ||_p$ the induced Matrixnorm for $1 \leq p \leq \infty$. Is it true that
$$||A||_p\leq \max(||A||_1,||A||_{\infty})?$$
For $p=2$ the answer is yes because ...

**0**

votes

**1**answer

263 views

### solving trace norm equality [closed]

Problem Formulation
under what conditions can we solve $\mathrm{trace}(\mathbf{AB})=0$ ? or more specifically, when will $\mathrm{trace}(\mathbf{AB})=0$ implies that $\mathrm{trace}(\mathbf{B})=0$.
...

**1**

vote

**0**answers

87 views

### expansion with respect to p-norms for p other than 2

Suppose I have an $d$-regular expander graph with $n$ vertices, where the stochastic version of its adjacency matrix $A$ (with entries $1/d$ and zero) has second eigenvalue $\lambda$.
Let $x \in ...