# Questions tagged [linear-algebra]

Questions about Mathematica functionality related to manipulating vector spaces and linear mappings between such spaces. This includes determination of matrix properties, matrix transformations, decompositions, and factoring.

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### Finding invariant matrix given group elements

I have a question about speeding up / optimising the following calculation. I have a feeling there is a way to rewrite it but I can't quite see what to do. In $d=3$ dimensions, given a set of ...
25 views

### How to select the column of a matrix the proper way

One thing that is annoying in Mathematica is, selecting parts of a Matrix creates lists that do not retain the matrix structure. For example, in MATLAB if you do: A=rand(10,10) and then a=A(:,1) You ...
57 views

### What is the fastest way to get the lowest eigenvalue and corresponding eigenstate in Mathematica?

I tried to use the Arnoldi method to get the smallest eigenvalue and corresponding eigenstate for large matrix. However, Arnoldi did not give me the desired result: ...
470 views

### Factorize trigonometric matrices

Consider two square matrices $A_1$ and $A_2$. Consider the following matrix involving matrix trigonometric functions: \begin{equation} M_1(t)=\begin{bmatrix} \cos(tA_1) & t\mathrm{sinc}(t A_1) \\ ...
30 views

### finding a transpose matrix [duplicate]

sample = MatrixForm[ RandomVariate[NormalDistribution[0, 1.2], {3, 2, 2}]] Tranp = Transpose[MatrixForm[sample]] This is my attempt to find the transpose of ...
408 views

### Request for clarification of Eigensystem::eivn message

Bug introduced in 9.0 or earlier and fixed in version 11.0.1 What causes the problem of "two eigenvectors associated to one single multiplicity eigenvalue" that I am experiencing? After ...
697 views

### Speeding up the matrix exponential computation for sparse matrices

I want to compute the action of matrix exponential on a vector. My matrix $B$ is of a very large size and it is sparse, e.g., it is written as follows: ...
137 views

### How do I reduce to a basis?

I'm doing some computation with symbols X, Y, Z, XX, XY, ..., which are linearly independent elements in some larger vector space. For example, consider the ...
923 views

### What is the correct way to perform the Gram-Schmidt process?

I'm trying to do a simple processing in Mathematica. My original code was in MATLAB. Part of the computation is the Gram-Schmidt process, which is an iterative calculation. Every vector is changed ...
276 views

### Speed up the computation of the trace of a matrix

I have a symbolic symmetric $6\times6$ matrix: dim = 6; SetAttributes[s, Orderless] S = Array[s, {dim, dim}]; I want to compute the trace of $S^{12}$: ...
14 views

314 views

### Implementing positivity constraints over a six-dimensional hypercube

This question involves the same subject matter as my previous one (How can one achieve the most accurate estimates of certain six-dimensional integrals under specific constraints?), but with another (...
86 views

### How to compute matrices in Einstein notation:

I would like to compute $r_{ii'} = \sum_{kk'} A_{ii'}^{kk'} r_{kk'}$ where all indices vary from 0 to 1 to yield a vector / matrix.
257 views

### How to solve a linear system like that

I'm trying to reproduce the following result: with ...
54 views

### Having trouble coding my own QR decomposition using Gram Schmidt [closed]

I have this code for Gram Schmidt: ...
95 views

### QR decomposition using Gram Schmidt [closed]

First of all I don't want to use the reflection method, only Gram-Schmidt. So here's the program for Gram-Schmidt: ...