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
6 votes
1 answer
232 views
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 ...
- 231
0 votes
1 answer
97 views
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 ...
1 vote
1 answer
110 views
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 ...
- 11
0 votes
1 answer
86 views
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 ...
0 votes
0 answers
37 views
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 vote
1 answer
252 views
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 ...
- 169
3 votes
1 answer
135 views
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($...
- 145
0 votes
0 answers
105 views
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? ...
- 131
2 votes
0 answers
180 views
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 ...
- 21
4 votes
1 answer
140 views
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 ...
- 181
2 votes
1 answer
104 views
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 ...
1 vote
0 answers
57 views
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-...
- 121
3 votes
1 answer
199 views
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 ...
- 133
2 votes
1 answer
188 views
Implementation of the Lanczos algorithm
I tried to implement Lanczos' algorithm in Mathematica: ...
user45229
3 votes
1 answer
416 views
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 ...
- 33