Questions tagged [matrices]
For questions about construction and modification of matrices, objects represented by 2-dimensional arrays that are used to define linear operators within linear algebra.
358 questions
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Good algorithm to solve a system of "cyclic" banded linear equations
I would like to solve the equation $Ax=b$ where $A$ is an $N\times N$ "cyclic" banded matrix (there might be a better term, but I wasn't able to find it), i.e. a matrix that look like
$$\...
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Find coordinate in ordered-dithering matrix
The Bayer index matrix for ordered dithering can be computed as follows:
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Core reason for why fast MM would fail to work for Distance Product?
This continues a previous question
Usage of matrix multiplication for distance products
However, this time, my question focuses on the algebraic properties of the classical mm and the min-plus/...
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How to quickly compute power of matrix of generating functions?
I have a 2x2 matrix of generating functions which I want to raise to a large power $m$:
$$\begin{bmatrix}
a(x) & b(x)\\
c(x) & d(x)
\end{bmatrix}^m.$$
I then want to retrieve the first $n$ ...
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Knuth's Algorithm X for edge matching puzzles matrix definition
I'm learning a great new stuff and one of the things is Knuth's Algorithm X, which is super simple but an interesting different viewpoint at the problem. Of course this is a great application for ...
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Algorithm Discovery Using ChatGPT O3-mini-high?
I gave this prompt to ChatGPT o3-mini-high: Give me a novel algorithm not discovered yet that reduces the complexity of matrix multiplication. Do you think this algorithm is correct and truly novel?
...
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Two vertical bars between 1xn matrix and a nonnegative integer in a cryptography paper
I am reading Indistinguishability Obfuscation from Well-founded Assumptions (pdf file) by Jain, Lin and Sahai, an important paper relating to program obfuscation in cryptography.
However, I think this ...
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Adam gradients for least squares approaches?
Least squares leads to an n-dimensional "parabola" in the parameters. I assume the same is valid for other constrained least squares like non-negative least-squares.
This may be a wrong ...
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Fastest algorithm to compute the nuclear norm
Given a matrix $A$ of size $k \times k$ over real numbers. The goal is to compute the nuclear norm (see this) of the matrix.
One way is to use SVD (singular value decomposition) and then calculate the ...
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Has anyone heard of "lifting diagrams" for matrix operations?
Currently studying colour space conversions for image representation. In my prof's slides, there's something he calls lifting diagrams:
They're just used to show matrix transformations, basically. ...
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Can you determine if a matrix can be made symmetric in poly time?
Is there an efficient way to tell if a square binary matrix can be made symmetric by reordering its rows and columns?
I can't see how graph isomorphism can be reduced to this problem so maybe there is ...
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Replace all elements of matrix with $x$ in minimum steps
This question was asked in a recent online assessment:
You are given an $n \times m$ matrix that contains $k$ unique elements. In one step, you can choose an element, and all occurrences of that ...
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Algorithm that sorts cells on the same distance clockwise
I am coding a board mini-game while learning java and I would like to find the most efficient algorithm to my problem (I found one but it looks inefficient).
Context :
The board is a x,y matrix ...
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For a matrix in a row-echelon form, what's a good algorithm to find the free variables?
Suppose I have a reduced row echelon form of a matrix for linear equations. The pivots from the corresponding Gaussian elimination are available. For example, in
$$
\begin{pmatrix}
1 & 0 & 0 \\...
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Straight forward algorithm for obtaining a sub matrix
Ok so I just started writing a linear algebra toolbox in C++ for some other projects I have / plan on starting in the future.
So I define a matrix as the fundamental building block and vectors, ...