Questions on the manipulation of matrices in Mathematica.

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4
votes
1answer
133 views

How to input and output partitioned matrices that show partitions and compute as normal?

I want to demonstrate multiplication of partitioned matrices as in the example here. Using the Insert Menu, you can build a matrix and draw lines between rows and columns. However, I want to be able ...
4
votes
3answers
315 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
3
votes
2answers
100 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...
3
votes
1answer
65 views

Computing kernels of a matrix in distinct cases

I have the following matrix: ...
2
votes
2answers
175 views

Matrix exponential via Cayley-Hamilton Theorem

I'm attempting to calculate the exponential of a matrix via Cayley-Hamilton theorem. (Following the "concrete example" from http://en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem) I am having ...
2
votes
3answers
156 views

Join matrix based on conditions

Given the following matrix: ...
1
vote
1answer
239 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
0
votes
2answers
160 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 = ...
30
votes
8answers
2k views

Longest path in 0/1 matrix

I have a matrix of 0's and 1's forming a number of disjoint paths:   I would like to find the lengths of the paths, and from that "spectrum," the longest length (in the above example: 27, ...
13
votes
1answer
497 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
15
votes
1answer
300 views

Unpacked eigenvectors of complex matrices

Edit: This bug is fixed in Mathematica 10.0.0 I want to calculate eigenvectors of a Hermitian matrix. For example ...
12
votes
4answers
437 views

How do you decompose a polynomial matrix into its matrix coefficients?

Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}} and I want to ...
8
votes
5answers
458 views

Is there a built in function to obtain the back diagonal of a matrix?

Given the following matrix: m = Array[Subscript[a, #, #2] &, {4, 4}] how can I find the skew diagonal or anti-diagonal or back diagonal of the matrix ...
19
votes
2answers
883 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 ...
6
votes
1answer
6k views

Quick Hessian matrix and gradient calculation?

I am absolutely new to Mathematica and I actually want to try implementing a little optimization method . Long story short assuming I have a predefined two-variable function f(x,y) I want to ...
7
votes
1answer
535 views

TensorContract of inverse matrix

Matrix inverse in mathematica If $A$ is an invertible $n \times n$ matrix, then $A\cdot A^{-1} = I$. To get this statement in Mathematica, you need the assumption ...
15
votes
5answers
646 views

How do I generate the upper triangular indices from a list?

I have some list {1,2,3}. How do I generate nested pairs such that I get {{1,2},{1,3},{2,3}}? That is I'd like a way to ...
14
votes
6answers
635 views

Matrix Rotation

If I have a matrix of any size, say $\begin{pmatrix} 72 & 32 & 64 \\ 18 & 8 & 16 \\ 63 & 28 & 56 \\ \end{pmatrix}$ $\begin{pmatrix} 72 & 32 \\ 18 & 8 \\ 63 ...
12
votes
6answers
634 views

Elegantly split a matrix into positive and negative parts?

I have a matrix $M$ of real components, and I want to split it into two matrices $M^+$ and $M^-$ of the same dimensions as $M$, where $M^+$ contains the positive components of $M$ (the remaining ...
9
votes
2answers
328 views

Speed up 4D matrix/array generation

I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way ...
8
votes
4answers
320 views

Fast method to select matrix elements based on a vector of positions

There is an operation for which I have long wanted to find a better solution. Let: a be a matrix of dimensions $m\times n$ ...
8
votes
5answers
345 views

correct way to map a function on entries down the pages in a 3D matrix?

updated: added another method to the methods I tried below for completion. This is new way of doing it, but most likely not very efficient, did not time it I can only visualize 3D matrices in my ...
7
votes
4answers
523 views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
7
votes
1answer
472 views

Extract matrix from a system of linear equations [duplicate]

I have a big system of linear equations $f_i(x_1,...x_n)$ with $n$ variables and $n$ equations. I want to extract the matrix $M$ where $\vec{f}(\vec{x})=M\vec{x}$. For example if I have $$ f_1(x) = x ...
6
votes
3answers
232 views

Need help with plotting triple data points while xy data are not regular?

recently I plotted some figure in matlab whose quality is not so satisfactory, so I come to mathematica as my supervisor suggested. This is how it looks like in matlab:. In matlab I have three m by n ...
5
votes
5answers
320 views

What is the fastest way to replace all zeros in a matrix?

In the following matrix m every 0 should be replaced with a 1: m = {{0,1,2},{5,0,3},{8,0,0}} Desired result: ...
4
votes
2answers
829 views

A dot appearing after a zero, and making the entries of a matrix into fractions

For more info about the difference between 0. and 0 I am a self-taught Mathematica user and I have some elementary questions-- perhaps too elementary for this site, but here they are. If ...
3
votes
1answer
317 views

How can I get Mathematica to recognize equality of symbolic matrix expressions?

I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ...
12
votes
4answers
327 views

Inputting a big structured matrix in Mathematica

Hi this is my first post and this is a problem that has bothered me a lot. Suppose we have the $2012\times2012$ square matrix: ...
10
votes
1answer
202 views

Compose many Geometric Transformations for 3D Graphics

I'm struggling to understand what would be a good way to compose several geometrical transformations to create a single TransformationFunction to be applied to a ...
9
votes
1answer
398 views

Mathematica implementation of Earth Movers Distance?

Has anyone implemented in Mathematica the Earth Mover's Distance (EMD)? A concept dating back to Monge 1871, used to compare histograms and images, e.g., the CIEDE2000 Color Difference algorithm. ...
8
votes
8answers
709 views

Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
8
votes
2answers
512 views

How to generate a matrix group?

I have three $7\times 7$ matrices (with real entries, lots of zeros) and I'd like to check if they generate a finite group (or, more precisely, if the group they generate is of precise order). Would ...
8
votes
2answers
260 views

Correct way to generate large data sets (i.e.forward yield curve )

I would like to generate a set of forward yield curve matrix of size 1000 x 100. First I defined my SparseArray of 1000 x100: ...
6
votes
2answers
420 views

Combining three R, G, B matrices into a single matrix of 3-tuples?

Working with Mathematica 8 on OSX here. I have three $1024 \times 1024$ matrices representing the counts from consecutive exposures onto a CCD with $R$, $G$, and $B$ filters on it, and am looking to ...
6
votes
2answers
695 views

Has Mathematica a function to compute the Smith Normal Form?

The Smith normal form is a matrix that can be calculated for any matrix (not necessarily square) with integer entries. See Wikipedia for a more elaborate description. Has Mathematica a function to ...
4
votes
2answers
189 views

Time-efficient creation of matrix

I have expressions like xx1=FF[1, 1] GG[1, 1] + FF[1, 1] GG[2, 2] + FF[2, 2] GG[2, 2] xx2=2*FF[1, 2] GG[1, 1] + FF[1, 1] GG[1, 2] + FF[2, 2] GG[2, 2] and I want ...
4
votes
2answers
2k views

I need to multiply a series of matrices

I need to perform a dot product on a large number of 2 x 2 matrices that I have defined to differ by even/odd subscripts (Ex: D-odd=x but D-even=y). The $\Pi$ function will not work because it does ...
4
votes
2answers
528 views

Loop and do operations on Matrix, then graph the results

I'm trying to do some operations to a matrix in a loop, and then I want to graph the results. The results are pair of numbers. Can I store the results of each iteration on "something" and the use ...
3
votes
0answers
78 views

Understanding polyharmonic splines

Raul Narain and J.M. gives implementation of the thin plate polyharmonic splines in this post. Raul Narian's method is clear. J.M.'s is convenient to reuse. But J.M. used too many ...
3
votes
1answer
233 views

Is there any faster way than Eigensystem to diagonalize a Hermitian matrix?

Is there any faster way than using "Eigensystem" to diagonalize(get all the eigenvectors and eigenvalues) of a Hermitian(self-adjoint) matrix? That would be amazing :). Thanks.
3
votes
1answer
394 views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
3
votes
1answer
827 views

stationary distribution of a transition matrix

How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition matrix?
2
votes
3answers
2k views

Passing a matrix as a function argument

I am trying to do the following: ...
0
votes
6answers
200 views

How to build a game board [duplicate]

I have - rather lazily - constructed a chessboard like this: ...
8
votes
1answer
393 views

Efficiently Constructing Rank One Approximations for a Matrix using SVD

Suppose I have a $m\times n$ matrix $A$ (real for simplicity). Then SingularValueDecomposition[A] yields 3 matrices $U$, $\Sigma$ and $V$ such that $A = U\Sigma ...
7
votes
5answers
191 views

Selecting terms from a matrix

There are similar questions to this on the forum but none fit the purpose here: I would like to extract certain elements of a matrix depending on whether a factor is present or not, and create ...
7
votes
3answers
409 views

How do we solve N-Rooks variation using primes?

Using a $p_n $x $p_n$ matrix, how can we solve the N-Rooks problem to find a prime in every row and column? ...
6
votes
4answers
318 views

Counting adjacent elements in a Matrix?

To start, I have a situation where I have some matrix, for example $$ A=\left[ \begin{matrix} 4&2&2&3&3\\ 2&3&1&2&3\\ 3&0&4&0&4\\ ...
6
votes
1answer
673 views

vectorial ODE in mathematica with matrix exponentials

I want to solve the following equation in mathematica : DSolve[{X'[t] == A.X[t], X[0] == ( {{0},{0}} )}, X[t], t] It is a system of 2 ODEs coupled by the matrix A, ...