# Questions tagged [nonnegative-matrices]

A non-negative matrix is one whose entries are non-negative.

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### Positive / negative (and so on) definite matrix. Confusion about the terms

I have problems in understanding the terminology used in Sylvester's Criterion about the "sign" of a matrix. I got the "positive-definite", the "negative-definite", the &...
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### Efficiently Finding a Rotation that Makes a Set of Vectors with Arbitrary Entries Non-Negative

Given a set of $k$ vectors ${x_1, x_2, ..., x_k} \in \mathbb{R}^n$ with arbitrary entries, we seek an efficient algorithm to compute an orthogonal matrix $Q \in \mathbb{R}^{n \times n}$ that can ...
133 views

### Intuition of $D\leftarrow XC^{T}\text{diag}(C1_n)^{-1}$ update rule in matrix factorization

I am reading this paper where they use Matrix Factorization over Attention mechanism in their Hamburger model. In section 2.2.2 they say, Vector Quantization (VQ) (Gray & Neuhoff, 1998), a ...
53 views

### Rewriting $||x-y|-z|$, for non-negative $x$, $y$, $z$, in a way that does not involve nested absolutes

Is there an idea that resolves nested value expressions into several separate expressions each using a single absolute value? Something similar like resolving the max function using the absolute value....
130 views

### Can the kernel of a quasi-positive matrix contain a positive vector?

Let $A$ a $n\times n$ quasi-positive matrix, i.e. $A$ has all non-negative entries $\ge 0$ and exists $n > 0$ such that $A^n$ is positive. We further assume that it has a $0$ eigenvalue, whose ...
1 vote
51 views

### Spectral Radius of Perturbed Matrix

Let $A$ be an n-dimensional square matrix such that each entry of $A$ lies in $[0,1]$, i.e., $a_{ij} \in [0,1]$ for all $1\le i,j\le n$. Let $\widetilde{A}$ be a perturbed version of $A$ where some ...
1 vote
62 views

### Number of positive and zero entries in doubly stochastic matrices

I have been researching doubly stochastic matrix properties, but didn't find proof of pretty known fact, so I would like to ask it here. How to prove the following? A doubly stochastic matrix Cannot ...
107 views

### Dimension of the fixed space of stochastic matrices (reference request)

Let $A \in \mathbb{R}^{d \times d}$ be row stochastic (i.e., all entries of $A$ are $\ge 0$, and each row sums up to $1$. Let $G(A)$ denote the directed graph that is associated to $A$, i.e., $G(A)$ ...
31 views

### Can we determine whether a symmetric matrix appended by one column/row maintains the Perron-Frobenius property?

Assume we are given a symmetric,non-negative, irreducible matrix $A \in \mathbb{R}^{n \times n}$. Then by the Perron-Frobenius theorem, there exists an eigenvector $v \in \mathbb{R}^n$ for the ...
Consider some compact set $K$ and the space of continuos functions $C(K,\mathbb{R})$. We obviously can define an algebra on this space by defining multiplication as $fg(i) = f(i) g(i)$ A band $B$ is ...