# 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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### Possible Bug in LinearSolveFunction with Sparse Vectors

Bug introduced in 5.0 and persists through 10.4.1 LinearSolveFunction is new in 5.0 Consider the following set of equations and corresponding variables: ...
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### Plotting Invariant Manifolds of the Henon Map

Given the following map: \begin{align} & x_{n+1}=-y_n+2x_n^2 \\ & y_{n+1}=\beta x_n \end{align} for $β \in (0,1)$, $x_n \in \mathbb{R}, y_n \in \mathbb{R}$ (which is a one parameter version ...
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### Working with matrix

Considering the 3x3 matrix: m = {{0, -(I/Sqrt[2]), 0}, {I/Sqrt[2], 0, -(I/Sqrt[2])}, {0, I/Sqrt[2], 0}} How would I find its normalized vectors eigenvectors u_i ...
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### Why does Eigenvalues work for a matrix $\{M\}$ but not $\{\{M\}\}$?

Suppose I have a matrix {{1, 2}, {3, 4}} which I'll call mat. In a blur of human error, I computed the eigenvalues of ...
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### Is it possible to speedup these simple linear algebra operations

I'm trying to numerically solve some equations using splitting operator method. The solver I construct iteratively constructs a matrix and feeds it to LinearSolve. ...
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### What's the most “functional” way to do Cholesky decomposition?

I can do Cholesky in a procedural style, such as: ...
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### Issue in Det[…] when computing determinants of polynomials?

When I form a matrix of at least size $12 \times 12$ of second order polynomials in $w$ and I calculate the determinant of that, I get something that is a rational expression in $w$. Since the ...
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### Bilinear Dot Function

In mathematics the matrix product is a bilinear operation $$\alpha A \cdot(\beta B + \gamma C) = \alpha\beta ( A \cdot B )+ \alpha \gamma (A\cdot C ),$$ where capital letters denote matrices and ...
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### How to plot several functions without jumping? (multiple eigenvalues of a system as functions of 2 parameters)

I've been working on this research problem for months with some success by no global/proper solution to the problem. So I have square, Hermitian matrices of various sizes ($8,20,38$ dimensions) with ...
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### Change of basis of polynomials

Suppose I have a favourite basis for polynomials in $x_1,\dotsc,x_n$, say non-symmetric Macdonald polynomials to be specific. I can easily compute these, and thus the change-of-basis matrix that takes ...
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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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### Finding most general matrices $A$ and $B$ such that $A\cdot B=1$

I would like to find the most general shape of matrices $A$ and $B$ such that $A\cdot B=1_{4\times4}$. Naively, I just define for example ...
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### Varying constant in Matrix calculation to generate 3D plot

As suggested, I rewrite my code to make it simpler and directly showing the problem. Here is a short example. I'd like to generate 3D plot where x,y,z (= a,b,answer) while I am varying a (0 ...
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### Transform set of linear equations into matrix and two vectors

Consider a list L containing entries dependent on variables x[i] (the i are integer, yet not ...
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### Repeated multiplication of a square matrix and a column vector in Mathematica

I am very new to Mathematica and StackExchange, so pardon me if I am repeating a question that has already been answered. I am trying to use Mathematica to do the following: u[n+1] = A.u[n] where A is ...
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### Expressing the n-th power of a matrix [duplicate]

My matrix is $\qquad A= \begin{pmatrix} {1} & {2} & {3}\\ {4} & {1} & {0}\\ {0} & {5} & {4} \end{pmatrix}$ I need $\qquad A^n$ I tried ...