# Tagged Questions

The tag has no usage guidance.

77 views

### Closed form solution for optimization problem

Consider the problem of finding the real-valued matrix $C$ so that $$\|S-AC\|_F^2\qquad(1)$$ is minimal. ($S$ and $A$ are real valued matrices and $_F$ denotes the Frobenius norm). This problem has ...
25 views

36 views

2k views

### What parts of linear algebra are used in computer science?

I've been reading Linear Algebra and its Applications to help understand computer science material (mainly machine learning), but I'm concerned that a lot of the information isn't useful to CS. For ...
81 views

### Efficient computation of Kronecker product

Given matrices $A \in \mathbb{C}^{n_1,m_1}, B \in \mathbb{C}^{n_2,m_2}$ a naive way to computer the Kronecker product would be as such: $M = \operatorname{zeros}(n_1n_2,m_1m_2)$ (initialize an empty ...
35 views

### What is the exact definition of a dictionary in the concept of linear algebra and computer science?

I am reading this paper for my master thesis and trying to understand every concept in it. The following sentence confuses me as to what is the exact definition of a dictionary in this concept except ...
126 views

### Generate algorithmically all grid points inside a hypercube

$\def\R{\mathbb{R}}\def\Z{\mathbb{Z}}\def\n#1{\|#1\|_\infty}$The problem comes directly from computational mathematics, and can be stated as follows: Given a regular matrix $M\in\R^{d\times d}$, find ...
34 views

### Partially diagonalizing a matrix

Suppose I have a $n\times n$ matrix. I would like to keep an $m\times m$ subblock undiagonized, while keeping the rest diagonized. Is there any algorithm for this? More precise, I mean using unitary ...
73 views

### Feasibility of linear inequalities with binomial variables

I have a system of linear inequalities of the form $A^t x <= b$ where each of the $x_i$'s is a binary variable in $\{0, 1\}$. Are there any known fast and practical algorithms that can find a ...
136 views

### Complexity of Pythagorean triples

We define a Pythagorean triple as a triple $\langle a,b,c\rangle$ such that $a,b,c\in \mathbb N$ and $a^2+b^2=c^2$. In order to avoid duplicates, we say that a triple $\langle a,b,c\rangle$ is legit ...
494 views

### Proof of Strong Duality Via Farkas Lemma

I am trying to prove what is often titled the strong duality theorem. There is a hint in the book that I'm following, and I want to follow the method they have outlined for me. I will outline the ...
284 views

### What algorithms exist for solving natural number linear systems?

I'm looking at the following problem: Given $n$-dimensional vectors of natural numbers $v_1, \ldots, v_m$ and some input vector $u$, is $u$ a linear combination of the $v_i$'s with natural number ...