Questions tagged [matrix]
For questions about using and representing matrices on a computer in order to solve computational problems. Should generally also include a tag about the specific property/problem you are solving (e.g. [tag:linear-algebra], [tag:eigenvalues], [tag:inverse].
645 questions
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Feasibility of computing large determinants
I have a dense $10^6\times10^6$ matrix having entries in $[-2^m+1,2^m-1]\cap\mathbb Z$.
What resources do I require in $2025$ state of the art for computing the determinant in a reasonable time of say ...
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Scaling of a matrix based on leading order terms
I am working in computational mechanics and I am working on a semi analytical solution for fracture in curved thin shells. I am implementing the solution in Matlab.
TL;DR: are there strategies to ...
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1
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Euler Angle Compression
CONTEXT FOR THE QUESTION
I'm porting animations between two video games from the same developer that use mostly the same skeleton and coordinate system. So in general, data can be ported from the ...
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How to transform the matrix into a specific form
Consider a full-row rank matrix $A \in \mathbb{C}^{r \times n}$ (where the number of rows r is less than the number of columns n). How can we find a column permutation or an invertible transformation ...
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Matrix transformation [duplicate]
Consider a full-row rank matrix $A \in \mathbb{C}^{3 \times 7}$,How can we find a column permutation or an invertible transformation T such that TA has the following form:
$
\left[
\begin{array}{...
1
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1
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Fast implementation to numerically find the nearest positive semi definite matrix, for a slightly non-PSD matrix
I have read
Numerically find the nearest positive semi definite matrix to a symmetric matrix
and
How to find the nearest/a near positive definite from a given matrix?
But the key problem is I need to ...
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3
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1
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Basis change of a 4D tensor / tensor contraction
I am from chemistry background so please bear with me with my silly question.
I have a tensor($\Gamma_{ijkl}$) which is in Molecular orbital basis. I am trying to transform it to Atomic orbital basis($...
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Why do two equivalent expressions yield different numerical results when using differentiation matrices?
I am computing an expression numerically in two different ways and obtaining a non-zero result when taking the difference between the two. Can you please help me understand the discrepancy?
...
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2
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How to compute eigenvalues of a large symmetric complex matrix (100k x 100k) on a GPU?
I need to compute all the eigenvalues of a large symmetric complex matrix on a GPU. The matrix has dimensions 100,000 × 100,000, with double-complex precision values. This means it requires 160GB of ...
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1
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How is the basis change computed in alternative basis strassen's algorithm for matrix multiplication?
Crossposted on Mathematics SE
A recent paper proposed the Alternative Basis Strassen algorithm [1] for matrix multiplication, which uses 7 multiplications and 12 additions, but needs you to make a ...
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2
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1
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How do you check convergence for an ill-conditioned system?
I am following along in Leveque's book on finite difference methods, and struggle on the stop condition for solving $Au = f$, where $A$ is the five-point stencil with periodic boundary conditions and ...
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Why does MOM fail for large number of subdivision for finite dipole?
In Constantine A. Balanis' book about antennas, he introduced the method of moments for current distribution over a finite dipole.
I found that the method of moments works very bad for a half-...
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1
answer
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Algorithm to compute the canonical form of a (skew-)symmetric matrix pencil
Let $A, B$ be $2n \times 2n$ complex skew-symmetric matrices. There exists a canonical form for the pencil $A - \lambda B$, related to the Kronecker canonical form (which itself is a generalization of ...
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2
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1
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Implementation of the Lanczos algorithm
I tried to implement Lanczos' algorithm in Mathematica:
...
user45229
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1
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Efficiently Updating Matrix Multiplication Result When One Matrix Changes
Suppose you have two matrices $A \in Z_q^{m\times l}$ and $B \in Z_q^{l\times n}$, and the product $A\cdot B$ has already been computed. Now, matrix $B$ remains unchanged, but a few elements in matrix ...
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