2022 Developer Survey is open! Take survey.

# Questions tagged [linear-algebra]

Linear algebra deals with vector spaces and linear transformations.

212 questions
Filter by
Sorted by
Tagged with
153 views

1 vote
104 views

### Is this proof of $LP$ being in $coNP$ correct?

I am referring to the natural decision version of the Linear Programming problem: given $A \in \mathbb{Q}^{m \times n}, \ b \in \mathbb{Q}^m, \ c \in \mathbb{Q}^n, \ \alpha \in \mathbb{Q}$, does there ...
62 views

### Precise rank of a sparse integer matrix

Consider a large sparse rectangular integer matrix. Is there a way to compute its exact rank that is better in terms of speed and/or memory usage compared to a dense matrix?
116 views

### Solver for uniform matroid isomorphism

I want to solve the following coNP-complete problem efficiently in practice: Given a linear matroid represented as $k \times n$ matrix over a finite field $\mathbb{F}_p$ (where $p$ is large prime), ...
60 views

### Problem conditions to use Laplacian solvers

I am trying to use Laplacian Solvers to solve a linear equation. I am just learning it (form here), so my question is very basic and it might not even make sense. Suppose that we want to solve Ax=b, ...
24 views

### Looking for information about a problem of a least subset of vectors modulo 2 summing to another vector [duplicate]

I'm quite interested in the following algorithmic problem, on which I can't find any information. Phrased as a decision problem: Given a set of vectors $V$ in $\text{GF}(2)^n$, a vector $\mathbf u$ ...
109 views

### efficiently computing a sum of products of polynomials

Let $F$ be a prime finite field. Let $d$ be a power of two dividing $p-1$. Suppose I have $d$ pairs of univariate polynomials $f_i,g_i$ over $F$ for $i=1,\ldots,d$. All have degree less than $d$. I ...
1 vote
51 views

### Complexity Lower Bounds for 3D Sparse Gaussian Elimination

I'm interested in lower bounds on the complexity in the real-RAM model of solving systems of linear equations which have the sparsity pattern of a three-dimensional cubic mesh. Specifically, consider ...
229 views

223 views

### The complexity of the permanent of low rank matrices

I know that for an arbitrary $n \times n$ matrix, Ryser's algorithm can compute the permanent in $\mathcal{O}(2^n n^2)$ time. I'm interested in computing the permanent of $n \times n$ matrices of rank ...
157 views

### Algebraic methods for testing planarity

Mac Lane's planarity criterion states that a graph is planar if and only if it has a cycle basis such that each edge is contained in at most two cycles, we call such a basis a 2-basis. A 2-basis of a ...
208 views

### What are some good resources for strengthening my theoretical foundation for machine learning?

I'm a computer science major and I'm taking a lot of machine learning courses. I'm finding that my theoretical foundation on subjects like calculus and linear algebra are not as strong as I'd like ...
5k views

### Evidence that matrix multiplication is not in $O(n^2\log^kn)$ time

It is commonly believed that for all $\epsilon > 0$, it is possible to multiply two $n \times n$ matrices in $O(n^{2 + \epsilon})$ time. Some discussion is here. I have asked some people who are ...
167 views

493 views

90 views

### Some consequences of the Roychowdhury-Orlitsky-Siu result from 1994

This pertains to the proof of theorem 1.1 in this paper, http://dl.acm.org/citation.cfm?id=2897636 So Roychowdhury-Orlitsky-Siu had shown that the number of depth $2$ linear threshold gate circuits ...
65 views

### A random ensemble of sparse boundary operators

The following question arises from the study of quantum error correction, and high-dimensional expanders: Is there an algorithm that for given numbers $n>0,d≤n,r≤n$ samples uniformly a linear ...
Recently in this beautiful paper, https://arxiv.org/pdf/1705.02397.pdf it has been shown that there is an explicit $Th \circ Th$ function with sign-rank scaling exponentially in dimension. I wanted to ...