Questions on the linear algebra functionality of Mathematica.

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0
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0answers
36 views

Solving a system of equations over a custom domain [on hold]

I'm trying to solve a system of linear equations with a large number of variables, but Mathematica is having real trouble finding solutions in a reasonable amount of time. One thing I thought would ...
2
votes
1answer
1k views

Solve matrix equation A*X=X*B using LeastSquares

I want to solve matrix equation A*X=X*B using LeastSquares method, but it is suited for equation like A*X=B. All matrices are 3x3 ...
6
votes
2answers
180 views

How to estimate the matrix condition number in the 2-Norm?

The Mathematica documentation say it is possible to estimate the Matrix condition number in norm 1, 2, Infinity. But the 2-Norm raise a message. This is an extract from reference documentation ...
0
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0answers
29 views

How to solve equations over polynomial rings

sorry if my question is very basic but I don't know what to even search to look it up and the only "obvious" places I thought of had nothing. Some background, for whatever context it might provide. ...
0
votes
1answer
70 views

How to power-series expand determinants?

Say $g$ is a matrix which is given as, $g = g_0 + xg_2 + x^2 g_4 .. +x^{d/2 -1}g_{d-2}+ x^{d/2}(g_d + h_d(log (x)))$ where $d$ is an even number and each $g_i$ is a matrix (same dimension as $g$) and ...
0
votes
1answer
84 views

LinearSolve failing to find solution to system of linear equations of 64 variables

I've got a 64x64 Matrix L for which I want to find the solution to the matrix equation L . x == rho. L is defined as ...
5
votes
6answers
629 views

A matrix-vector cross product

I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$. ...
2
votes
1answer
85 views

Matrix constructed as a function inside a for-loop [closed]

I am trying to construct a matrix A which depends on variables x and y through iteration. My ...
0
votes
1answer
69 views

eigenvector bug also for matrix with numeric value [closed]

I just realize that probably there is a bug also in calculating the eigenvector of a matrix with numeric values (see here for bug in eigenvector calculation with symbolic value). In particular in my ...
0
votes
2answers
49 views

Modifying elements of a matrix after construction [closed]

Suppose I have constructed a matrix with all elements as a constant (say 1): N=4; A=ConstantArray[1, {N, N}]; Now I want to make A(2,3)=23 and A(4,3)=43. Can I ...
0
votes
0answers
24 views

SVD (Singular value decomposition) for matrix with constant row sum and column sum [migrated]

M is a m*n matrix, the row sum equals to (K/m) and the column sum equals to (K/n). After SVD, we can find three matrix U,S,V, M=USV where U,V are orthogonal matrix and S is diagonal matrix. I can ...
3
votes
1answer
119 views

How get eigenvectors without phase jump?

I'm using Eigenvectors to get the eigenvectors for some matrixes, but the eigenvectors seems to have some phase jump. Here is an example: Say we have a 2 by 2 ...
0
votes
1answer
53 views

Any command for group products?

Is there any Mathematica command or well known technique to take the direct product between two symmetric/permutation groups?
1
vote
1answer
72 views

how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
0
votes
1answer
120 views

Differences between 'Solve' and 'LinearSolve' [closed]

Using the function 'Solve' I can do the following: Solve[a x + y == 7 && b x - y == 1, {x, y}] I get the following output: I want to get the same output using 'LinearSolve' instead. How ...
3
votes
1answer
146 views

Control over the way matrix is displayed

I am wondering how to change the output format in Mathematica. For example, I have $x=\binom{3}{1}$ and $y=\binom{2}{5}$, and I want to find what linear combination of $x$ and $y$ produces ...
1
vote
1answer
103 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
2
votes
1answer
55 views

How to Normalise / Normalize eigenvectors? [closed]

I have a matrix and am trying to find the normalised eigenvectors of it. I am using the Eigensystem command and am getting a result. There is a normalize command, but as far as I can see this ...
1
vote
0answers
65 views

The Jacobi-Davidson method

Does any implementation of the Jacobi-Davidson method for Mathematica exist? A highly parallelized version for sparse matrices would be of special interest.
0
votes
1answer
128 views

How to create a 2D array (matrix) [closed]

I am pretty new to Mathematica. I need to create 2d array dynamicly. I got some code in C++(Qt) and it looks like this: ...
1
vote
1answer
46 views

Correctly substituting a matrix into a scalar equation [duplicate]

I am having trouble correctly substituting a matrix into an (originally) scalar equation. For example: A = {{3, 1}, {1, 2}} cp = CharacteristicPolynomial[A, x] ...
1
vote
1answer
47 views

Simplification of linear algebra [duplicate]

I have a few vectors defined as V1 = Array[v1,3] V2 = Array[v2,3] V3 = Array[v3,3] And I am trying to solve a very simple equation along the lines of ...
1
vote
0answers
68 views

Diagonalization in parallel

I would like to diagonalize one unitary non-sparse matrix of size 12870 with complex number entries (not symbols, this is really a numerical problem). Is is possible to make eigensystem run in ...
1
vote
0answers
63 views

Find eigenvalues without filling the matrix

Is it possible to find eigenvalues of a matrix without filling it? The matrix elements are given by a known function f[p1,p2]. This is relevant for a matrix too ...
2
votes
3answers
222 views

Treat strings as variables?

I have a list of strings, {"x1", "x2", "x3", "x4"} And a list of linear equations: ...
5
votes
3answers
502 views

How to solve an eigensystem faster?

I have a module that I need to call 1-10 million times in my program. Currently, it is taking several hours to run so I am hoping that I can cut down some runtime with your help. ...
0
votes
0answers
61 views

Is there a way to solve the linear equation, Ax=b, in which A is a “non-constant” sparse matrix that depends on x?

I want to solve the Linear Equation, $Ax=b$ in Mathematica using Kylov subspace solver method preferably BICGSTAB(http://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method). Suppose ...
11
votes
2answers
492 views
8
votes
1answer
151 views

Is there a built-in procedure for simultaneous diagonalization of a set of commuting matrices?

Given a set $\{A_1,...,A_m\}$ of $m$ commuting $N\times N$ diagonalizable matrices, it is known that there exists a basis of eigenvectors $\Lambda$ that simultaneously diagonalizes all the $A_i$. Is ...
1
vote
1answer
157 views

Traces of products of Pauli matrices

Given a matrix $M$ of shape $2^L*2^L$, I would like to compute all the traces $\text{Tr}( M.(\sigma^{n_1}\otimes\sigma^{n_2}\otimes\ldots\otimes\sigma^{n_L})) $ for $n_1=1...4$, $n_2=1...4$, ..., ...
23
votes
3answers
3k views

Can Mathematica do symbolic linear algebra?

For instance, is there some way I can say "let A and B be arbitrary real $m\times n$ and $k\times m$ matrices, Simplify[Transpose[Transpose[A].Transpose[B]]]" and ...
2
votes
1answer
49 views

How to distribute PermutationProduct over the sum

Assuming I have two elements of the permutation group algebra $a_1$, $a_2$ such that $a_i=\sum_{p\in S_n}\alpha_pp$, I want to define a linear product $\odot$ that distributes over the sum and pulls ...
4
votes
0answers
760 views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
0
votes
0answers
43 views

How to get integer/rational and real eigenvectors to be the same? [duplicate]

forgive me if I missed this already being answered or too easy. Given a matrix: q = {{1, 3, 5}, {7, 11, 13}, {1/3, 1/7, 1/13}}; Eigenvectors are different here: ...
0
votes
1answer
190 views

Symbolic Jacobian computation

I have an equation for which I would like to compute the Jacobian symbolically. $$f(x)=Ax-diag(x)(Ax+b)$$, where $x\in \mathbb{R}^n$, $A\in \mathbb{R}^{n\times n}$ and $b\in \mathbb{R}^n$. I am new ...
0
votes
1answer
135 views

Simplify matrix into an upper triangular matrix

I have a tridiagonal matrix that I am trying to simplify into an upper triangular matrix using Mathematica, so I can use back substitution and solve my linear system. I have found the command ...
2
votes
1answer
91 views

Problem with Eigenvectors when given a matrix containing approximate numbers and symbols

I'm trying to diagonalize a certain 2 x 2 matrix, but Mathematica refuses to find the eigenvectors. In particular, when I input ...
1
vote
1answer
69 views

Efficient calculation of diagonal matrix elements

I have a matrix $V$ of size $M$ in which each row $i$ is a vector $v_i$. Now I have another matrix $H$ and I would like to calculate as efficiently as possible the list of values $v_i^\dagger\cdot ...
4
votes
3answers
239 views

Approximate minimum degree permutation algorithm in Mathematica

In MATLAB there is a nice implementation of the so called AMD (approximate minimum degree permutation) algorithm named amd (see Online MATLAB Documentation). There is an alternative algorithm called ...
0
votes
2answers
152 views

Eigenvector Anomaly

I'm trying to compute the eigenvectors for: $$ M = \left( \begin{array}{ccc} 1 & 4 \\ 4 & 100 \end{array} \right) $$ Both myself and Mathematica report the eigenvalues as: $$ \lambda_1 = ...
1
vote
0answers
74 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 ...
1
vote
2answers
237 views

Using the epsilon tensor in Mathematica

I'm having a great deal of trouble getting started on a weekly homework assignment in Mathematica. The assignment requires we use the epsilon tensor which is apparently built into Mathematica as ...
6
votes
1answer
334 views

Find the eigenvector associated with the smallest eigenvalue, not smallest in magnitude

I am trying to find the eigenvector of a $20000 \times 20000$ sparse matrix associated with the smallest eigenvalue. I realized that the smallest eigenvalue might be negative; for example, if the ...
7
votes
1answer
371 views

What type of solver does Mathematica use in LinearSolve

I have a question regarding linear equation solvers. For a specific 9x9 diagonal matrix, every method I tried in C++ (Gaus, GCC, BICGTAB ) wouldn't work, although these methods would work fine for ...
0
votes
0answers
45 views

Addition of sparse array objects [duplicate]

I have been having some trouble with the addition of large (but very sparse) matrices using SparseArray. Here is the simplest example to illustrate the issue. First, I will define diagonal matrices ...
13
votes
1answer
389 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
10
votes
3answers
696 views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
2
votes
2answers
258 views

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 ...
0
votes
0answers
64 views

Memory issue when using LinearSolve

When I use LinearSolve to solve a large system of linear equations where the left hand side is a matrix and the right hand side is a vector, the process takes a ...
1
vote
1answer
123 views

What is most efficient way to convert system of equations to collection of functions?

I have the type of system M.x = b, where M is a known matrix and b is a known vector. M contains many parameters, call the entire parameter set 'a', so M => M[a]. I want to be able to efficiently ...