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# Questions tagged [linear-algebra]

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### Computational Complexity of Integer Linear Program [with Fixed number of 'Pure Constants']

This is a follow up to the previous Question: Conditions for Linear Diophantine Equations to always have a solution It was established in the above's answer that obtaining or testing for the ...
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### small size and small depth circuit for set intersections

Input: Given sets $S_i \subseteq \{1,2,3,4,\cdots,n\}$ for $1 \leq i \leq n$. Output: sets intersection with restriction (pick first set $S_1$. If $a \in S_1$ such that $a$ is the least element then ...
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### Finding dimensions of a point cloud - floating point issues

I have $N$ data points of some dimension $D$. I want to know the dimension of the shape that those data points represent - for instance they might be a 2 dimensional triangle, even though they are in ...
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### Properties of coset

Let $C$ be a linear code with minimum distance $2k$. I want to show that there is a coset of $C$ that contains at least two vectors of weight $k$. Firstly, it holds that the minimum distance of the ...
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### Minimise simultaneous equation remainder

I'm not sure if this is the right place to ask, or what the right terminology to use is. The problem I have is this: I have a vector for example: v = [1,4,5,6,3,1,4,5,6,7,...7] and I have a set of ...
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### Partially diagonalizing a matrix

Suppose I have an $n\times n$ matrix. I would like to keep an $m\times m$ subblock undiagonized, while keeping the rest diagonized. Is there any algorithm for this? More precisely, I mean using ...
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### Recover boolean vector from dot products

Question: I want to determine a boolean vector $b \in \{0,1\}^n$ consisting of zeros and ones, but cannot access it directly. I can only call a black-box computer code which will take the dot product ...
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### Representing chained XOR operations as linear inequalities

I'm trying to solve an integer linear program (ILP) in which a constraint of the following kind must be met: $x_1 \oplus x_2 \oplus \cdots \oplus x_n = 1$ where $\oplus$ is the binary xor operator. ...
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### Complexity of matrix inverse via Gaussian elimination

I'm trying to determine the exact complexity of finding an $n\times n$ matrix inverse of $A$. If it is known that the complexity of Gaussian elimination is $\frac{2}{3}n^3 + \frac{1}{2}n^2+O(n)$, then ...
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### Scheduling distributed computational graph

I work in computational fluid dynamics. And I spend most of my time waiting for simulation to complete. The common way to improve simulation performance is to use a suitable distributed linear ...
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