Questions on the manipulation of matrices in Mathematica.

learn more… | top users | synonyms (1)

3
votes
3answers
140 views

Chopping matrix elements, real or imaginary

An undesired shape of a matrix has the following form: which is created by ...
26
votes
5answers
965 views

Can (compiled) matrix permanent evaluation be further sped-up?

Update III  Mathematica 10.2.0 now ships with a predefined System`Permanent function, which the PermanentCode package ...
11
votes
3answers
1k views

Correcting a correlation matrix to be positive semidefinite

Does Mathematica have a way to "fix" a correlation matrix that is not positive semi-definite? I looked through the documentation and search the internet but could not find anything.
3
votes
4answers
513 views

How to transform this matrix & swap its columns in a simple way?

I would like to transform matrix $\mathbf A = \begin{pmatrix} a&b&i&j\\ c&d&k&l \\ e&f&m&n \\ g&h&o&p \end{pmatrix}$ into matrix $\mathbf B = \begin{...
12
votes
7answers
644 views

Brackets around each item in matrix

I have a matrix where every item in the matrix has its own brackets that I do not want. How can I remove the brackets around each item?
9
votes
7answers
2k 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.
16
votes
4answers
2k views

What is the right way to rotate an array?

Suppose I have an array, not necessarily square: a = $\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right)$ I want to rotate it like one ...
12
votes
1answer
838 views

How to extract and replace submatrix of a doubly-periodic matrix?

How can I effectively extract and replace a rectangular subpart of a toroidal matrix, i.e. one where boundaries are connected at opposite ends? Since the submatrix can overhang the edges, a simple <...
11
votes
3answers
1k views

How can I visualize 6 square matrices as a cube?

I have six square matrices of the same dimensions in a list, for example: ...
11
votes
3answers
528 views

How do you concatenate matrices? And how do you make block matrices?

This is pretty trivial to do in Matlab, but I have not seen a function for it in Mathematica. Here is how you can do it with Join and ...
10
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 "...
4
votes
4answers
535 views

Listing matrices up to symmetry

I am interested in the equivalence relation on N x N binary matrices, in which two matrices are equivalent if one can be obtained by rotating/reflecting the other. I would like to obtain a list ...
3
votes
1answer
79 views

Formatting All Appropriate Output as Desired Automatically

I want to output in MatrixForm whenever I have a list/vector/matrix, but I do not want to have to type out the command each time. How can I write one command at ...
3
votes
2answers
934 views

All possible solutions to the Matrix Equation (free variables appearing)

I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
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... <...
8
votes
8answers
761 views

Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
6
votes
2answers
741 views

How to combine elements of two matrices?

Given two matrices m1 and m2, e.g.: m1 = {{a1, b1}, {c1, d1}} m2 = {{a2, b2}, {c2, d2}} How can one obtain the following? ...
4
votes
4answers
318 views

Elegant Matrix Combinations

Suppose you have a matrix (mxn), simplified for illustration m= {{a, b, c}, {d, e, f}} And a set of combinations (simplified for illustration purposes but can ...
4
votes
2answers
98 views

replacement in a nested matrix

We have a nested matrix m1 = {{{1, 2, 2, I}, {1, 1, -2, 1}, {3, 2, 2, -I}}, {{3, 4, 4, I}, {1, 1, 4, 1}, {3, 3, 4, -1}}}; we must replace the first number of ...
3
votes
1answer
677 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 ...
2
votes
1answer
583 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 ...
6
votes
2answers
347 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 ...
6
votes
3answers
648 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. ...
5
votes
2answers
125 views

Comparison Operation for Nested Matrices

I have a nested matrix n as bellow ...
5
votes
4answers
159 views

Add to matrix missing elements (for list of time series)

This question is an extension of the 43122. I’ve looked through many interesting post (like this) but (as always) missed the direct matching. So the setting is simple: ...
5
votes
3answers
190 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?
4
votes
2answers
132 views

Factor out the scalar multiplier for the dot product of 2x2 matrices

If yy and zz are 2x2 Hermitian matrices, is there a way that I can mark them (with a property?) as Hermitian so that Mathematica can assume that it can factor out and simplify scalar multipliers from ...
4
votes
3answers
1k views

Orthonormalization of non-hermitian matrix eigenvectors

When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
4
votes
1answer
222 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 ...
3
votes
1answer
78 views

Computing kernels of a matrix in distinct cases

I have the following matrix: ...
3
votes
3answers
385 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 ...
3
votes
1answer
154 views

different situations with Compilation of ConstantArray

First, we load some tools related to Compile for analysis. ...
2
votes
3answers
187 views

Join matrix based on conditions

Given the following matrix: ...
2
votes
1answer
700 views

Why is EigenValues returning Root expressions? [duplicate]

This is the code I have: ...
2
votes
2answers
588 views

Create a matrix of matrices using Band and ArrayFlatten [duplicate]

I can easily write a simple Band matrix using: SparseArray[{Band[{2, 1}] -> a}, {Dim, Dim}] where a is a number. Now, I ...
2
votes
3answers
85 views

How to get an element of a list , which is computed out of substituted variables?

What is the best way to get the element of a list, which is computed out of substituded variables? For example one wants to get the first element of the first row of ...
1
vote
3answers
90 views

Percent Difference between elements from 2 matrices

If i have a 22 by 25 table of values which depend on n and r, and a list of values that depends on r that is a 22 by 1 matrix, how can I find the percent difference between each element, by row in the ...
1
vote
2answers
2k 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 ...
1
vote
2answers
163 views

Partitioned matrix operations

I have a $(2 \times 2)$ matrix whose elements are themselves $(2 \times 2)$ matrices (i.e., a partitioned matrix), e.g: $$ M = \begin{pmatrix} A & B \\ C & D \end{pmatrix}, \quad \quad \text{...
1
vote
1answer
727 views

How to add an extra column to a current matrix (list)? [duplicate]

a = {{-800, 1712}, {-801, 1713}, {-806, 1832}} TableForm[a] b = a[[All, 2]] - Min[a[[All, 2]]] How do I make a new matrix (list) whic looks like this ...
26
votes
1answer
2k views

Is there a way to convert an image into a Graph?

I'm trying to convert an image with several overlapping dots into a Graph. The goal is to be able to derive the Kirchhoff matrix for the randomly created "network ...
23
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 ...
33
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, ...
15
votes
5answers
551 views

A quicker than outer

I need to get a matrix $\{a(x_i-x_j)\}$, where $x_i$ form a partition of an interval, $a(x)$ is a given function. I use ...
13
votes
1answer
918 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
16
votes
3answers
565 views

Compiling LinearSolve[] or creating a compilable procedural version of it

Earlier today I had a discussion with a representative at Premier Support about the 2 questions I've asked here over the past couple of days: Seeking strategies to deploy a function securely ...
9
votes
5answers
1k 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 (...
17
votes
1answer
374 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 ...
14
votes
4answers
638 views

Decomposing a matrix with polynomial elements into a polynomial with 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 ...
11
votes
2answers
309 views