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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1answer
45 views

How to find selected elements of inverse of a banded matrix without inverting it?

Is it possible to find some selected elements of the inverse of a large sparse matrix without inverting it? For example consider this Hermitian matrix (as a general case). ...
0
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1answer
50 views

LinearSolve on non-square matrices?

I just came across a strange behaviour for LinearSolve (on Mathematica 8.0.0.0). Consider the following definitions: ...
1
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1answer
76 views

What's is the restrictions for the function MatrixExp?

When I use the MatrixExp on a general $2\times2$ matrix, Mathematica gives me this result: MatrixExp[{{a,b},{c,d}}] // TraditionalForm ...
0
votes
0answers
64 views

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 ...
5
votes
3answers
118 views

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 ...
0
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1answer
60 views

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 ...
4
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1answer
59 views

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 ...
2
votes
2answers
118 views

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 ...
11
votes
2answers
376 views

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 ...
0
votes
1answer
102 views

Precision of Eigensystem? [closed]

I was using Eigensystem to obtain the rotation matrix. However, I find out Mathematica does not fully diagonalize my matrix (or say not precise enough). My matrix ...
6
votes
2answers
412 views

Does Eigenvalues evaluate in a parallelized way?

I use mathematica on a computer with linux operating system. The computer has 2 cpus and each cpu has 4 cores, so there are totally 8 cores available. Now I got confused with whether the evaluation ...
1
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2answers
518 views

Get inverse of a matrix step-by-step [duplicate]

How can I get the inverse of a matrix step by step? An example: Given the matrix `{{8, 2}, {3, 2}}´, the result is {{$\frac{1}{5}$, -$\frac{1}{5}$}, {-$\frac{3}{10}$, $\frac{4}{5}$}}. But how can I ...
7
votes
1answer
161 views

What kind of Arnoldi method is used in Mathematica?

Can someone give me a bit more information about what mathematical method Mathematica is using, (preconditioner, filtering-restarting, deflation) in the Lanczos implementation when I input something ...
5
votes
0answers
144 views
3
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0answers
147 views

Mathematica's Singular Value Decomposition different from another math engine [closed]

I’ve been working with SVD – singular value decomposition. Things weren’t working as expected. Thus, I looked over to Matlab and executed the following code: ...
3
votes
2answers
391 views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } ...
9
votes
1answer
101 views

UnitaryMatrixQ function not returning true for a unitary matrix

So I know this matrix is unitary. It's a well proven fact in quantum mechanics and you can even check for yourself on pen and paper, Heres a quick proof: Assume $H$ is hermitian (i.e. $H^\dagger=H$) ...
0
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0answers
59 views

Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
1
vote
1answer
44 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
43 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
171 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
147 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
59 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
216 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
47 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
0answers
94 views

Constructing the coefficient matrix in discretization of a PDE

In order to solve the following two dimensional PDE $$\frac{\partial u(x,y,t)}{\partial t}-\frac{1}{2} \sigma _1^2 x^2 \frac{\partial ^2u(x,y,t)}{\partial x\, \partial x}-\frac{1}{2} \sigma _2^2 y^2 ...
3
votes
2answers
52 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, ...
24
votes
5answers
913 views

Can (compiled) matrix permanent evaluation be further sped-up?

Update III  Mathematica 10.2.0 now ships with a predefined System`Permanent function, which the PermanentCode package ...
2
votes
1answer
82 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
71 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: $y_{n \times 1}$, ...
4
votes
3answers
146 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
33 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
101 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
514 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
132 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 ...
7
votes
1answer
224 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
41 views

Tolerance of PositiveSemidefiniteMatrixQ [closed]

I believe the following should be True but returns False for me: ...
0
votes
1answer
91 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 ...
0
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0answers
67 views
2
votes
1answer
59 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
141 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
77 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 ...
19
votes
2answers
334 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
69 views

Reliably computing the signature of a matrix with small eigenvalues

When asked to compute the eigenvalues of the following matrix ...
0
votes
1answer
44 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
154 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 ...