Questions on the manipulation of matrices in Mathematica.

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5
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1answer
681 views

Matrix Rational Canonical Form

Is there a way to calculate the Rational Canonical Form of an $n\times n$ integer matrix using Mathematica? I have been perusing the documentation and web, but nothing so far.
5
votes
4answers
197 views

Split matrix by all-zero columns

Below is my input: mat = {{0, 0, 0, 0, 0, 1}, {1, 0, 0, 1, 0, 1}, {0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1}, {1, 1, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 1}}; ...
1
vote
1answer
61 views

Sort and Save Matrices Eigenvectors to a Larger Matrix

We are going to sort and save all orthoginalized-eigenvectors of 4*4 random matrices (produced in any iteration) to a larger matrix such as storagematrix. Since, produced random matrices are 4*4, ...
2
votes
0answers
85 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
3
votes
1answer
149 views

Mathematica error code 0x00000171

I'm getting above error code with a Trap 132 indication when attempting an ArrayPlot of a complex 130000 x 2048 matrix. Using Mathematica 9.0.1 with Mac OS 10.10.3 ...
9
votes
3answers
1k 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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0answers
65 views

How do I diagonalize a matrix? [closed]

How do I diagonalize the following matrix: ...
1
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0answers
54 views

How to remove parts of an expression

I have an expression where terms Transpose[R].R appear. R is a matrix with the property Transpose[R].R=IdentityMatrix[3]. How ...
5
votes
1answer
205 views

Distribute transpose on matrix multiplication

I need to do the following: Transpose[A.(B+C)]=Transpose[B].Transpose[A]+Transpose[C].Transpose[A] How should I do this in mathematica? So far mathematica does ...
36
votes
2answers
948 views

eigenvector bug?

Bug introduced in 7.0.1 or earlier and fixed in 10.0.0 I have a fairly simple $3\times3$ complex matrix, $$ M=\left( \begin{array}{ccc} \frac{7}{2}-\frac{i}{2} & -1+i & \frac{1}{2}+\frac{5 ...
1
vote
1answer
78 views

Calculating a multiplication of large number of matrices takes a long time [duplicate]

I have a multiplication of matrices, say M1.G1.M2.G2.....Mn.Gn, here n may reach 100. M and G are 4 4 matrices and their elements are function of s. Mathematica takes so long to perform this ...
4
votes
0answers
107 views

How can I force the use of sparse diagonalization methods?

When I evaluate the Eigenvalues function on a very large (e.g. 2^16 x 2^16) sparse matrix, Mathematica says something like: Because finding 65536 out of the ...
0
votes
2answers
99 views

Matrixform ndsolve for mobile robot dynamic equations

Error is: NDSolve::ndsdtc: The time constraint of 1.` seconds was exceeded trying to solve for derivatives, so the system will be treated as a system of differential-algebraic equations. You ...
0
votes
0answers
37 views
1
vote
1answer
88 views

Transposition of state space form of a transfer function

How can I transpose the output of state space model in Mathematica? trying the following code would transpose the top right symbol s instead of the matrices. ...
9
votes
2answers
1k views

How to transform a 3D image by an affine transformation matrix

I have a question concerning Image Processing: I have a stack of images, which I can compose to a 3D image using Image3D. Additionally I have a 4x4 affine transformation matrix. I would like to ...
1
vote
1answer
82 views

multiplication of 4*4 matrices whose elements are function of x and y [closed]

I have a matrix 4*4 M whose elements are a function of x and y. I would like to multiply this matrix for different values of x and y, say M[1,1].M[2,2]......M[n,n]. How I can do it?
25
votes
1answer
294 views

Does Mathematica store hidden information for matrix objects?

Bug introduced in 10.0 and fixed in 10.2.0 I found a case where calling one built-in function (HermitianMatrixQ) for a given matrix changes the behavior of ...
2
votes
1answer
73 views

Problem with NDSolve and Sign

If c1 cnd c2 are zero, the code responds very well; but if one of c1 or ...
6
votes
3answers
213 views

On a strange pattern of triangular numbers in Ulam's spiral

In this MSE post, user GeMir noticed that, where the green dots are the triangular numbers, $$T_n = \frac{n(n+1)}{2} = 1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,\dots$$ in the Ulam spiral ...
2
votes
1answer
74 views

Extract Transfer Matrix from TransferFunctionModel

I have a MIMO transfer function model, and I'd like to know how to perform arithmetic on this model. For instance, to see the difference between two systems' outputs for arbitrary inputs, I'd like to ...
5
votes
3answers
270 views

Huge matrices crashes in Mathematica

I have a matrix of data ~(70,000x70,000). I am searching connection between these data points. I use euclidean distance for that purpose. If it is less than my threshold (that means they have ...
9
votes
4answers
350 views

Finding the position of similar elements in a matrix

I want to find the position of the elements which are equal in a matrix. For example in the case of the following matrix: $m =\left( \begin{array}{cc} a & x \\ x & a \\ \end{array} \right)$ ...
9
votes
3answers
2k views

Why don't * and ^ work as I expected on matrices?

For example, this input... {{1, 2}, {3, 4}}*{{1, 2}, {3, 4}} produces this output... {{1, 4}, {9, 16}} and this input... ...
0
votes
3answers
220 views

Calculating eigenvalues of a large matrix takes a long time

I have a tridiagonal matrix (1000×1000) with each element equal to $1$ except {n, n} = 2. It takes 8 hours to give me the eigenvalues?!! Here is the code I used: ...
1
vote
1answer
88 views

Handle matrices and vectors with general dimension

I have a matrix of $n \times n$ dimension: $$ K - \omega^2 M = \begin{pmatrix} 2\omega_0^2 - \omega^2 & - \omega_0^2 & 0 & \cdots & 0 \\ - \omega_0^2 & 2\omega_0^2 - \omega^2 ...
8
votes
3answers
792 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} ...
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vote
0answers
41 views

Diagonal times dense matrix, high precision

I have a fixed dense matrix M of high precision numbers, say 40 by 40 and precision 40. Then I have a variable vector v of the ...
1
vote
1answer
74 views

Displaying a matrix with integral entries

I have a matrix nxn with coefficients a[i,j] like: a[i,j]=NIntegrate[T[r], {r, -le, le}] - NIntegrate[T[r] Abs[r]/le, {r, -le, le}] I can solve the matrix but I ...
1
vote
0answers
29 views

Function to be used for spectral decompostion of matrix [duplicate]

Can anybody please help in finding out what is best way to do spectral decomposition (or Eigen decomposition) of the matrix. The details of Eigen decomposition can be found in attached link 1. ...
2
votes
0answers
75 views

MatrixRank of a large but sparse matrix

I want to find the rank of a very sparse, quite rectangular matrix mat, but I'm running out of RAM (I have 16 GB) if I try to use ...
22
votes
2answers
1k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
3
votes
3answers
286 views

Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
1
vote
1answer
102 views

Matrix multiplication for higher dimensional matrices [duplicate]

I have a matrix like this (myb1): I would like to get the matrix multiplication of each of the submatrix to itself. For example the first 2x2 matrix $\begin{bmatrix}1 & 2\\1 & ...
1
vote
2answers
219 views

Having trouble translating Matlab `fsolve` into Mathematica

I searched the site and found that someone said FindRoot is equivalent to fsolve, however, without proper options, ...
3
votes
1answer
147 views

Programming for matrix manipulation

I want to write a programme which operates on nd x nd matrices. The programme looks the matrix as a n x n block matrix where ...
1
vote
1answer
120 views

Multiplying three matrices does not give expected form [closed]

I'm having lectures on analytic geometry. I've learned that there is an associated matrix multiplication for a quadratic form: $\quad \quad \left( \begin{array}{ccc} x & y & 1 \\ \end{array} ...
3
votes
1answer
84 views

Eigenvalues function not producing expected results?

I'm running into a strange issue when trying to compute eigenvalues of a 2x2 matrix for graphene. If I "manually diagonalise" by multiplying the two off-diagonal terms together and taking the square ...
2
votes
0answers
33 views

How to get simultaneous eigenvectors of commuting matrices? [duplicate]

So let's say there are two square matrices A and B that commute (AB-BA=0). This implies that there must exist some complete set of vectors that are eigenvectors of both A and B. Is there any way to ...
1
vote
1answer
40 views

Can I rely on the ordering of the adjacency matrix? [closed]

Suppose I have created a Graph[{1,2..n}, {1->3, etc}], and I take the adjacency matrix of that graph. Can I rely on the fact that the i-th entry in the graph is the i-th node in the matrix? Or maybe ...
0
votes
2answers
42 views

How to get Complement function working in a For loop? [closed]

I've been working on a piece of code that will delete small components from a nested uneven matrix (n pages, n rows, 3 columns), by deleting the pages with less than ~30 rows. However, I've notice ...
1
vote
0answers
49 views

Does a matrix need to be rationalized when calculating MatrixExp? [closed]

I have a sparse matrix, L, and need to calculate its exponential, MatrixExp[L t], where t is ...
3
votes
3answers
206 views

Matrix with known entries but unknown size [closed]

I am trying to perform some calculations with a matrix that has let's say size N but unknown, please How can I write this in mathematica?
0
votes
1answer
73 views

Elements inside arrays seem to be strings rather than signed numbers

When I have code like b = Array[Subscript[be, #] &, {3, 1}] b = b /. {Subscript[be, k_] :> Subscript[-be, k] /; k > 1} I am noticing that Mathematica ...
3
votes
1answer
114 views

How to tell Mathematica that my variable is a scalar

In my calculations I have these combinations PauliMatrix[1].f PauliMatrix[2] where f is a scalar function. The result is as ...
5
votes
0answers
388 views

How to invert a matrix with 100 trillion elements?

I have a $10^{7}\times 10^{7}$ matrix with the following properties: it is sparse it is gamma-5 it is almost Hermitian. If $M$ is the matrix we are trying to invert, we know $M=A M^{\dagger} A$ ...
0
votes
1answer
89 views

Symbolic matrix calculation [closed]

I have question about a matrix calculation like $\mathbf{b}^{t}\,\Sigma\,\mathbf{b}$, where $\Sigma$ is a 7 by 7 matrix, and $\mathbf{b}$ is vector of 7 elements, and each element in the vector ...