Questions on the linear algebra functionality of Mathematica.

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0answers
76 views

Symbolic Nullspace computation in parallel

I am trying to determine the nullspace of a large symbolic matrix. The single core evolution seems to take too long. I tried Parallelize[] on the commands ...
3
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1answer
81 views

Graphs Plotting Discontinuous

I'm trying to plot a graph from the eigenvalues of a matrix I created. The graph shows with discontinuities in it and I was looking for some feedback. Here's the code: ...
0
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1answer
94 views

How large can be the dimension of a complex matrix which Mathematica can handle to find its eigenalues?

I have been working with 12 cross 12 complex matrix in Mathematica , I need to work with bigger size matrix of the dimension of the order of hundreds , I was wondering if Mathematica can handle ...
0
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1answer
88 views

Submatrix with linearly independent columns

What I want is the submatrix where all the linearly dependent rows have been eliminated. I tried implementing this solution, but it doesn't work in the following example: ...
1
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1answer
178 views

Basis for the intersection of vector spaces

The MuPAD Notebook Interface provides the linalg::intBasis function: http://www.mathworks.com/help/symbolic/mupad_ref/linalg-intbasis.html How can I get the same ...
4
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3answers
135 views

A Product function for matrix products

I would like to use an equivalent of the product-function in mathematica, but where instead of multiplying numbers I multiply matrices?
0
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1answer
36 views

I need help simplifying this equation [closed]

1 = D / R Now I want to add a value to each side. U. Is it like this? 1 + U = D / R + U Then I need it simplified. Thanks
1
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2answers
92 views

Using conditionals to check if LinearSolve found a solution

Is there some way to check if LinearSolve found a solution using conditionals in Mathematica 9? I need to solve a large number of linear equations, but I am only interested in the cases where there ...
0
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1answer
68 views

How to tell Eigensystem the type of the elements comprising a matrix I would like to diagonalize

How can I tell Eigensystem that a matrix $M$, which I would like to diagonalize, is a numerical matrix of complex numbers? My idea is that this information could ...
1
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0answers
89 views

Request for clarification of Eigensystem::eivn message

What causes the problem of "two eigenvectors associated to one single multiplicity eigenvalue" that I am experiencing? After several transformations to simplify an unwieldy matrix, I end up with the ...
2
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1answer
157 views

Sort eigenvectors of a list of matrices

I have a list of matrices and want to obtain a list of eigenvectors and eigenvalues for each matrix, both sorted by the size of the eigenvalue. If I write ...
4
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3answers
251 views

What is the best way to write a polynomial in the Bernstein basis?

The Bernstein basis of polynomials of degree $n$ is the set of polynomials of the form $$\binom{n}{k} t^{n-k}(1-t)^k$$ where $0 \leq k \leq n$. What is the best way to transform a given polynomial ...
3
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1answer
204 views

Find the NullSpace of a matrix whose determinant is “almost” zero

If $A$ is a matrix such that $\det(A)=0$, it is easy to get a basis of the kernel of $A$ with NullSpace[A]. Now let's consider a matrix $B$, function of a ...
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1answer
308 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the question Symbolic matrices in Mathematica with unknown dimensions provides a functionality to create symbolic matrices which behave pretty much as the name suggests. ...
13
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1answer
444 views

Morphological Filtering in 3D to produce skeletons

Context As a follow up of this question and that answer, I would like to identify the special lines separating 3D watersheds. These are useful in the context of astronomy to identify the ...
5
votes
3answers
165 views

Assuming reals of unknown variables in a Matrix valued function

I am trying to write a generic matrix valued function in a package, of the form: f[matrix_] := Module[...] My problem is that I want to accept any matrix, but ...
1
vote
1answer
149 views

Solving a System/Matrix of Equations in Matrix Form

Ok, I am trying to solve an equation involving matrices (well, tensors actually), which is of the form: $\mathbf{e}^{T} \cdot \mathbf{M} \cdot \mathbf{e}$ = $\mathbf{N}$, where $\mathbf{e}$ is an ...
1
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1answer
139 views

How smart is Solve? Figuring out what tricks I should try

I'm trying to solve a large system (~10000) of linear equations using Solve, but the process keeps failing. As-is, I don't know whether it's failing because it's using too much memory or too much time ...
1
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0answers
31 views

Symbolic computation under certain assumptions [duplicate]

Assume that I have a matrix $M$ and I'm doing some operations on it. Is there a way to specify that two variables satisfy an equation say $x=y^2$ and then let Mathematica compute under that ...
1
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0answers
105 views

Steps in row reduction? [closed]

I have a fully symbolic matrix that I'm row reducing. Looking at the end result, I see that Mathematica must have divided out some common factors for each row. However, I need to analyze those ...
3
votes
2answers
253 views

Intersection of two vector spaces

Is there a simple way without having to manually compute the matrices and do LinearSolve to do the following? Assume I'm given two lists $l_1$, $l_2$ of vectors of the same dimension. I want a list of ...
5
votes
1answer
500 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: ...
3
votes
1answer
137 views

Why does LinearSolve return the transpose of the answer matrix?

I am trying to solve an equation of the form $dv=F\cdot dV$ where $dv$ and $dV$ are matrices derived from the row vectors $dx$, $dy$, $dz$ and $dX$, $dY$, $dZ$ respectively. If it helps, $F$ is the ...
6
votes
2answers
480 views

Should eigenvalues be ordered?

When I run Eigensystem on a symmetric matrix, the list of eigenvalues (and so, the corresponding eigenvectors) is ordered by absolute values, which is quite bizarre (it does make sense if you view the ...
3
votes
0answers
247 views

Fast principal component analysis

I'd like to speed up a principal value value analysis. The data contains a large set of vectors with a large dimension. Both are in the range of 1000. I want to obtain the loadings matrix for further ...
3
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1answer
281 views
3
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1answer
64 views

How to pick out terms in a linear equation with a positive coefficient?

Basically I have a really large output which looks like a long linear equation $AAA-BAA-CAA+DAA+...-ZZZ$ And I only am concerned about those terms that have a positive coefficient (i.e. a plus in ...
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1answer
137 views

$SU(4)$ Structure constants in mathematica

How can I write a mathematica function which will output arbitrary structure constants of SU(4)?
2
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0answers
91 views

How to make Eigensystem in version 10 produce the same results as version 9 [duplicate]

The Eigensystem in version 10 seems to give slightly different results as in version 9: ...
7
votes
3answers
708 views

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

The Mathematica documentation says it is possible to estimate the matrix condition number in norms 1, 2, and ∞. But the 2-norm raises a message. This is an extract from reference documentation ...
1
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1answer
231 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 ...
9
votes
1answer
415 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
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1answer
72 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?
0
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1answer
142 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 ...
2
votes
1answer
131 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 ...
3
votes
1answer
273 views

Principal Components - how to obtain linear transformations?

I have a list "xlsf" with 6 columns and 1200 rows for PCA analysis. The PrincipalComponents[xlsf] gives the following: "The principal components of matrix are ...
3
votes
1answer
164 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 ...
2
votes
1answer
170 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] = ...
1
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0answers
111 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.
1
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1answer
50 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
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1answer
89 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
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0answers
153 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
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0answers
82 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
273 views

Treat strings as variables?

I have a list of strings, {"x1", "x2", "x3", "x4"} And a list of linear equations: ...
0
votes
0answers
197 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 ...
2
votes
1answer
401 views

Matrix exponential MatrixExp[] vs Sum[MatrixPower[]] doesn't match?

I might be an idiot, but I cannot get the manual expansion of $e^{At}$ to match the MatrixExp[A t] result. For example, I have the following: ...
11
votes
1answer
502 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 ...
2
votes
1answer
384 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 $n_1=1...4$, $n_2=1...4$, ..., ...
8
votes
3answers
634 views

Visualization of matrix transformations

I define the "matrix transformation" here as follows: $\left[ \begin{matrix} x_1' \\ x_2' \\ \end{matrix} \right]=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} ...
1
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0answers
45 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: ...