Questions on the manipulation of matrices in Mathematica.

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3
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2answers
1k views

Matrix multiplication in Block Form symbolic calculation by Mathematica

I have a problem which requires taking product of two $10\times10$ matrices. I would like to do it by considering both matrices as $5\times5$ matrices such that each entry of both matrices is actually ...
2
votes
1answer
445 views

RowReduce: Solving for the resource vector (a, b, c) in Augmented Matrix

Here are two examples: RowReduce[{{3, 1, a}, {2, 1, b}}] evaluates to {{1, 0, a - b}, {0, 1, -2 a + 3 b}} but ...
2
votes
3answers
2k views

Passing a matrix as a function argument

I am trying to do the following: ...
0
votes
2answers
165 views

Taking averages at certain intervals

I am trying to take averages of a large two dimensional array at certain intervals. For example, for the first row, I want to take K averages of 500 values. Here is what I am trying ...
5
votes
1answer
167 views

Is it possible to lower the bitwidth of (floating point) numbers?

The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits ...
5
votes
3answers
508 views

How to sum matrix elements based on finding the first (and second) non-zero elements of each row?

I have a matrix: I would like to sum all the first non-zero elements of each row so that I get a value of $$25.5317 + 8.85471 + 6.90018 + 32.9436 + ... $$ and so on and simply ignore zero rows. ...
4
votes
1answer
139 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
336 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
108 views

Eigenvectors of large symbolic matrix

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

Computing kernels of a matrix in distinct cases

I have the following matrix: ...
2
votes
3answers
193 views

How can I reproduce the MatrixForm, NumberForm, XyzForm behavior?

I wish to write a function like MatrixForm, that affect only display but not evaluation, i.e. a function that automatically is stripped away from output. More ...
2
votes
2answers
200 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
157 views

Join matrix based on conditions

Given the following matrix: ...
1
vote
1answer
260 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 ...
1
vote
2answers
1k views

large matrix eigenvalue problem

I need solve a very large complex matrix (not sparse and not symmetry) eigenvalue problem, e.g., 1e4*1e4 or even 1e6*1e6. How large dimensions of the matrix can Mathematica support? And, how about ...
0
votes
1answer
146 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 ...
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
557 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
8
votes
5answers
509 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 ...
15
votes
1answer
313 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
460 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 ...
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 ...
19
votes
2answers
970 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 ...
8
votes
5answers
885 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 ...
8
votes
7answers
1k views

How to select all elements above the main diagonal of matrix?

How to select all elements above the main diagonal of matrix? I need to create a list of them.
8
votes
1answer
588 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 ...
7
votes
1answer
560 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 ...
4
votes
3answers
768 views

Compute the rank of a matrix with variable entries

Say I have a matrix like $$ M=\left( \begin{array}{c c c} x & xz & w-2x \\ wz^3 & xy & z \\ y^2-z^3 & x+w & z+x^5 \end{array} \right) $$ is it possible to ask Mathematica ...
15
votes
6answers
671 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 ...
15
votes
5answers
660 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 ...
12
votes
6answers
647 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 ...
10
votes
1answer
416 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. ...
9
votes
2answers
347 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
362 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
366 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 ...
5
votes
5answers
366 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
1k 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
329 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
333 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
244 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 ...
10
votes
1answer
935 views

How to apply a permutation to a symmetric square matrix?

Given a symmetric square matrix, how can I apply a permutation to the rows and columns (i.e. the same permutation to both the rows and the columns) such a way that the new structure of the matrix ...
8
votes
8answers
721 views

Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
8
votes
2answers
578 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
265 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: ...
7
votes
3answers
298 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 ...
7
votes
2answers
821 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 ...
6
votes
2answers
445 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 ...
4
votes
2answers
190 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
551 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 ...