# Tagged Questions

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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### Eigenvectors choose intuitive ordering/sorting

Starting from some symmetric $L\times L$ matrices $M$(see below), I want to compute the eigenvectors in Mathematica, in order to construct an ...
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### LatticeReduce of a linearly dependent basis

l1 = {{-6327, 0, -2109}, {131, 0, -131}, {-6840, 0, 24929}}; LatticeReduce[l1]] returns {{1,0,0},{0,0,1}}. How do I find ...
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### more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559 + 1.682941969615793 I}, {2.161209223472559 - 1.682941969615793 I, 2}} and ...
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### Generate random Hermitian matrices [duplicate]

I want to generate random Hermitian matrices. For now, random Hermitian matrices with size 2 are obvious to construct. But elegant methods for higher dimension would be nice! Are there methods besides ...
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### Strange performance of Outer

The following takes 0.07 seconds on my laptop. list1 = RandomReal[1.,1000000]; (Outer[Times, list1, RandomReal[1., 2]];) // AbsoluteTiming But this takes 1.2 ...
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### Reduce set of symbolic equations to linearly independent subset

Given a set of symbolic equations $f_i(x_1,x_2,...,x_n)=0$ in several variables, for example f1=x+y-z; f2=x-y+z; f3=3x-y+z; I would like to apply a function <...
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### Does NDSolve automatically simplify the system of equations for Hermitian matices?

I am currently starting to solve numerically a system of differential equations like this: $\dot{A}(t)=S(A)A(t)$ Here, the matrices are of dimension $d\times d$. $S(A)$ is some superoperator that ...
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### “Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...