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.

learn more… | top users | synonyms

1
vote
1answer
46 views

Array Flattening arrays of matrices given by rules

Fix an $n$ and an $m$ positive integers.I have some set of four $n\times n$ matrices $A$,$B$,$Y$,$Z$ (where $Z$ is the zero matrix). I'd like to input the $nm\times nm$ matrix of block matrices given ...
3
votes
0answers
48 views

Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation (...
7
votes
1answer
197 views

Incorrect Left and Right Eigenvectors in Mathematica

I'm trying to find the Left and Right Eigenvectors of a pretty straightforward matrix, but Mathematica doesn't seem to be able to do it for even a 200 dimensional matrix. Background: Given an ...
4
votes
3answers
1k views

Orthonormalization of non-hermitian matrix eigenvectors

When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
4
votes
1answer
152 views

How do I disable that Mathematica orders terms in lexicographic order?

I have matrices with entries where the order of the entries is important. Unfortunately Mathematica resorts terms in products in a lexicographic order. For example, ...
0
votes
0answers
22 views

Rewriting List of Matrix Equation in Terms of Individual Equations? [duplicate]

I have a list of matrix equations M1={{a1,b1},{c1,d1}}; A1={{x1,y1},{z1,w1}}; M2={{a2,b2},{c2,d2}}; A2={{x2,y2},{z2,w2}}; sys={M1==A1,M2==A2}; which I would like ...
4
votes
1answer
61 views

Computing the logarithmic spectral norm rapidly

I wish to compute the logarithmic spectral norm of a square matrix $A$, which is defined by \begin{equation} \mu_2[A]=\lim_{t\downarrow0}\frac{\|I+tA\|_2-1}{t}. \end{equation} Hence, I simply code ...
1
vote
1answer
220 views

What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
0
votes
1answer
49 views

Solving simultaneous and determinant given constant value and variable T (temperature) [closed]

How to solve this two simultaneous equations? these two equations got from this free energy equation ...
3
votes
2answers
54 views

How to avoid 0 OverVector[F] to be evaluated as 0?

I am fairly new in Mathematica and I am trying to work with scalars and vectors. I decided to denote vectors using OverVector (as example, ...
2
votes
1answer
88 views

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 ...
1
vote
0answers
76 views

Deriving ordinary least squares (OLS) in matrix form

How can I instruct Mathematica to derive the OLS in matrix form with respect to $\beta$ and obtain the result ${-2X}^{T}(y-X\beta)$? The matrices have the following dimensions: $y_{n \times 1}$, $X_{...
4
votes
3answers
153 views

Write Sum of Matrices Explicitly

I have sum of lots of matrices A+B+C+D+E+... and I want that Mathematica shows me this as explicit matrix sum, i.e. Explicit Matrix A + Explicit Matrix B + Explicit Matrix C + .... and not just ...
3
votes
1answer
34 views

TensorContract with KroneckerProduct instead of ordinary Times

Is it possible somehow to contract two tensors, say A={{a1,a2,a3},{a4,a5,a6}} and B={b1,b2,b3}, where the elements ...
2
votes
1answer
115 views

Explicit Contraction of Tensor Indices [duplicate]

Is there any easy way to explicitly contract indices of several given tensors. For example, ...
5
votes
3answers
1k views

Generating random symmetric matrix

Suppose first that I want to generate a matrix whose elements are independent and identically distributed (i.i.d.) with distribution dist. This is easy: ...
13
votes
2answers
580 views

more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559` + 1.682941969615793` I}, {2.161209223472559` - 1.682941969615793` I, 2}} and ...
1
vote
2answers
134 views

LUDecomposition for non-square matrices

How do we go about finding the LUDecomposition for non-square matrices. When i try to input the standard LUDecomposition command,...
7
votes
1answer
225 views

How write a new MatrixRank feature with symbolic computation

The current MatrixRank is a slight foolish without any capacity of symbolic computation ,feature of Mathematica, like this: <...
0
votes
1answer
42 views

Tolerance of PositiveSemidefiniteMatrixQ [closed]

I believe the following should be True but returns False for me: ...
0
votes
1answer
120 views

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 ...
0
votes
0answers
34 views

Handling a matrix with components greater than machine precision

I have four quantities stemming from a 4th order differential equation. I can represent these as a vector which is a product of a 4X4 matrix $$ M=\left\{v,\frac{\partial v}{\partial x},\frac{\partial ...
1
vote
0answers
77 views
2
votes
1answer
60 views

Eigenvalues are not the same in the special case

I have this matrix: h = { {e1, 2, x}, {2, 2, x}, {x, x, 2} }; I want to calculate the eigenvalues and then set x equal to zero: ...
2
votes
3answers
145 views

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

Im trying to do a simple processing in Mathematica. My original code was in Matlab. Part of the computation is Gram-Schmidt process, which is an iterative calculation. Every vector is changed ...
-2
votes
1answer
82 views

How can I calculate $(y - A \,x)^{T}(y -A\,x)$ symbolically? [closed]

Given that $x$ and $y$ are column vectors and $A$ is a matrix, I figured out the result $y^{T}y-2y^{T}Ax +x^{T}A^{T}A\,x$ I want to use Mathematica to make such calculations. how do I enter them into ...
20
votes
2answers
352 views

How to know the usage of undocumented function like LinearAlgebra`BLAS?

BLAS is not documented in mathematica. Using ?LinearAlgebra`BLAS`* gives But None of the function has a detailed usage information Click any of the ...
2
votes
2answers
73 views

Reliably computing the signature of a matrix with small eigenvalues

When asked to compute the eigenvalues of the following matrix ...
0
votes
1answer
45 views

Strange eigenvector behaviour for matrix with large numerical values

I'm trying to compute the eigenvectors of a matrix with large numerical values $$ \left( \begin{array}{ccccc} 0 & 1.\times 10^{18} & 100 \text{X} & 0 & 1.\times 10^{11} \text{X} \\ ...
6
votes
1answer
156 views

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 ...
4
votes
3answers
172 views

How to plot real roots of complex polynomials avoiding branch cuts?

Lets say I have the following matrix: M={{1,3+E^(I x),-1+2I x},{3+E^(-I x),2,E^(3I x)},{-1-2I x,E^(-3I x),-2}}; $$ M=\begin{pmatrix} 1& 3+\mathrm e^{ix} &...
0
votes
1answer
173 views

Nonrectangular tensor encountered [closed]

I am trying to solve a system of equations which characteristic matrix: ...
3
votes
4answers
192 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
2
votes
0answers
116 views

How to solve lowest eigenvalue with Lanczos or Arnoldi algorithm? [closed]

By setting Method->Arnoldi in Eigensystem I was able to solve lowest eigenvalue and eigenstate of a large sparse matrix. ...
0
votes
1answer
120 views

Hermitian Matrix

From Derbyshire's Prime Obsession, I would like to get the Mathematica code to generate a Hermitian matrix for evaluation and display. $ 256 \times 256 $ would be nice. Random Normal distribution, ...
4
votes
0answers
146 views

strange timing result of LinearAlgebra`BLAS` in mathematica? [closed]

BLAS is short for "Basic Linear Algebra Subprograms". It is a famous collection of routines for doing linear algebra. I just know from Oleksandr R. that mma can directly call BLAS under the context "...
1
vote
2answers
99 views

Finding matrix given null space

Suppose I input a very large $n$ integer vectors and I wish to compute the matrix whose nullspace is spanned uniquely by these vectors. Is there an appropriate command/module to do this using ...
4
votes
2answers
147 views

How to be more efficient/faster with this MatrixExp-vector multiplication?

I am looking for expertise that helps to improve speed of the code below. First, a little bit of background: There is some system of differential equations $\dot{\vec{m}}(t)=S(t)\vec{m}(t)$. In order ...
0
votes
1answer
74 views

Minimization of linear combination of vectors

Suppose I have a vectors in $\mathbb{R}^{6}$. For example, take the vector $v = k(-2,2,4,6,2,2)$. I would like to find some $k$ with the constraint that the last two components are necessarily non-...
12
votes
2answers
4k views

Badly conditioned matrix (General::luc)

With some matrices, I am receiving the following message: ...
10
votes
0answers
117 views

Efficient solution of huge sparse linear system

I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
1
vote
0answers
50 views

Mapping over two indices with a condition

How can I use Map over two indices with a condition? I am trying to calculate second derivative of an eigenvalue, $\lambda_i(x)$, of $n \times n$ matrix $M(x)$ ...
9
votes
2answers
175 views

Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
2
votes
1answer
107 views

Is there a good way to check, whether a small value produced numerically is a symbolic zero?

I have a complicated 4x4 matrix and need to know the eigenvalues. I expect a zero eigenvalue for physical reasons. Giving numerical values first gives me an eigenvalue of $\mathcal O(10^{-15})$. Now ...
7
votes
1answer
91 views

Count degrees of freedom of a polynomial

I want to count the independent degrees of freedom of a polynomial in three variables $(z_0,z_1,z_2)$. Therefore I take the coefficients of $f$ and compute the rank Jacobian with respect to the ...
6
votes
1answer
182 views

Eigenvector Concern in Large Fractal-Like Matrix (Possible Bug?)

This is my first post and I have quite a long question. Thanks to any who read. To start with, I have an operator m=Transpose[n] on a 7 dimensional vector space V where n is constructed as follows: <...
1
vote
0answers
63 views

Multivariate Path Construction using Sobol numbers

I am sharing my code,which I have tried to perform as per the instruction mentioned below. Please correct it so that I could get my output. Instruction: Use the first m dimensions of the Sobol vector ...
1
vote
1answer
55 views
7
votes
2answers
409 views

Finding a unitary matrix in Mathematica

I have the following equation : $ \tilde{B} = U B U^{\dagger} $ I also know both $ B $ and $ \tilde{B} $ , I just want to find the matrix U, that gives me the transformation. I tried using ...
18
votes
1answer
487 views

Sparse Cholesky Decomposition

I am working with square matrices with a special form, which for large rank ($> 100,000$) would be best stored and manipulated as a SparseArray. I believe that ...