Questions on the manipulation of matrices in Mathematica.

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2
votes
1answer
163 views

An intuitive way to form an augmented matrix

Given an $m\times n$ matrix $A$ and a $m\times 1$ vector $b$, what is the most "intuitive" way of forming the augmented matrix $[ A\ b]$? The most concise way that I know of is ...
3
votes
1answer
64 views

Computing kernels of a matrix in distinct cases

I have the following matrix: ...
1
vote
1answer
140 views

Dirac Gamma matrix Algebra in different dimension

Do anyone know if we could do Dirac Gamma Matrix Algebra by FeynCalc with Gamma Matrices defined in different dimension than 4, e.g. DiracTrace of gamma matrices in 2+1 dimension? Thanks!
1
vote
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 ...
5
votes
3answers
269 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
vote
0answers
87 views

NMaximize with matrix input

I defined function f[x_, fixed_] := {...}. Here x is an $M\times N$ matrix. I want to maximize $f$ with respect to $x$. I have ...
1
vote
1answer
96 views

sequence of matrix multiplications

My linear algebra book has questions that are are marked to use math software. There's probably some $50 guide on how to do everything but usually documentation has gotten me through. I've been kind ...
59
votes
2answers
2k views

Flatten command: matrix as second argument

One thing I could never wrap my head around is how Flatten works when provided with a matrix as the second argument, and the Mathematica help isn't particularly ...
4
votes
1answer
153 views

Calculate the covariance of a large matrix

I have to compute the covariance of 50 very large integer matrices (2500x2000 elements). However, according to my estimation this will take around 10 days. Do you have any ideas how to speed things ...
14
votes
2answers
397 views

Better way to test that a matrix is upper-triangular?

Today, I got to thinking about how to test that a matrix was upper-triangular. So I had a try at it. Algorithm $\quad \quad a_{ij}=0 $ Or $i \leq j$ $\Rightarrow$ $True$ My solution is ...
2
votes
3answers
120 views

How to multiply specific columns in a matrix of data?

So I need to make a plot of some ~2000 data points I have from a spreadsheet. I'm able to import the data just fine, it stores it like so sundat ...
9
votes
3answers
897 views

An inverted pyramid

I want to draw a pyramid approximately like this ...
6
votes
3answers
224 views

Efficient method to generate Tridiagonal 50 by 50 Matrix? [duplicate]

I'm looking to generate a tridiagonal 50x50 matrix, ideally without using loops. Suggestions on most efficient code for this?
8
votes
3answers
319 views
3
votes
1answer
107 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 ...
31
votes
6answers
2k views

How to visualize/edit a big matrix as a table?

Is it possible to visualize/edit a big matrix as a table ? I often end up exporting/copying big tables to Excel for seeing them, but I would prefer to stay in Mathematica and have a similar view as in ...
2
votes
3answers
128 views

Syntax of transpose etc [closed]

This is a simple question: {{0, 1}, {0, 2}, {0, 3}}*Transpose[{{0, 1}, {0, 2}, {0, 3}}] returns an error in Mathematica but works perfectly fine in Wolfram Alpha. Can someone help me? Thanks so ...
9
votes
4answers
281 views

Replacing matrix values

I want to find the n largest values in a matrix and replace all others with zero. The solution I found uses ReplaceAll and becomes very slow as the size of ...
1
vote
1answer
111 views

Inverting matrix of unknown size

I have a matrix that has a variable number of columns and rows (but it is always square). The matrix is: $$ \Gamma = \begin{bmatrix} \Theta & 0 & 0 & 0 & T & 0 & R_j \\ ...
0
votes
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 ...
6
votes
3answers
101 views

How to create a block diagonal matrix by repeating a submatrix $n$ times?

If there is a submatrix, let's call $P$: $P=\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}$ And I want to have $n$, let's say $n=2$, such submatrices placed on the diagonal. The result is ...
3
votes
0answers
75 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 ...
0
votes
1answer
54 views

Combining lists in a matrix

So I have a list of data A={1.1,1.2,1.3,1.4,6.1} etc and B={2.5,2.6,2.7,2.8,2.9} I need to combine the lists into a matrix C ...
4
votes
1answer
104 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
2
votes
3answers
174 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 Ploev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
2
votes
0answers
55 views

CUDALink Error: A CUDALink kernel timed out?

I'm following the CUDALink tutorial [ http://reference.wolfram.com/language/CUDALink/tutorial/Introduction.html ] and everything is going fine until I get to the part that calls CUDADot on the ...
0
votes
6answers
195 views

How to build a game board [duplicate]

I have - rather lazily - constructed a chessboard like this: ...
3
votes
2answers
203 views

Order of eigenvectors [duplicate]

I have a matrix A = {{5, 4, 2}, {4, 5, 2}, {2, 2, 2}} The eigenvalues are 1, 1, 10 and I need to find the eigenvectors. ...
1
vote
1answer
62 views

m equations and n variables. Reducing using Mathematica

I have six equations and thirteen variables. I would like to reduce it to seven free parameters. I used Reduce to solve it but it is taking really long (one full day and no output yet) and I think ...
3
votes
2answers
275 views

How to create a 'shortest-path link matrix'?

I am currently struggling with a problem in Mathematica. I have a randomly generated weighted Barabasi-Albert graph and a corresponding demand matrix of the same size. I'm generating the graph with ...
15
votes
1answer
297 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 ...
0
votes
1answer
172 views

Defining a new matrix product of matrix function [closed]

Suppose I have two matrices A, B, whose entries are functions of x. Suppose they are 2*2. In the product, each entry is of the form $\sum_k A_ik B_kj$. There are two summands corresponding to k=1,k=2. ...
3
votes
3answers
121 views

Solving determinant of a Kronecker product of matrices gives a numerical error - why?

I am doing the following steps (code at the end of the post): I start with a 2x2 matrix (smatrix), which is a function of a single variable (u2). I want to set the determinant of this matrix ...
5
votes
2answers
1k views

How do I keep the right ordering of eigenvalues using Eigensystem?

I'm having an issue with the Eigensystem command. I need to diagonalize a bunch of 3 by 3 complex valued matrices, but more importantly, I need to keep the exact ...
4
votes
3answers
151 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}}; ...
13
votes
4answers
666 views

“Indexing” a vector

I need to "index" a vector according to the first occurence of its distinct elements. I have written ...
2
votes
2answers
104 views

Making a conjecture concerning a certain upper-triangular matrix

I have searched for commands which will let me to create matrices and do matrix operations, but I don't know how to apply Mathematica to the following exercise. Make a conjecture for the result of ...
0
votes
0answers
99 views

Spectral Clustering

I am interested in the following question: How is it possible to check whether an algorithm is working properly? However, this question is too general for the post and I'd like to restrict attention ...
5
votes
3answers
1k views

Matrix Multiplication in context of row and column vectors

I've been looking at some matrices in Mathematica and I've noticed something very weird: They're extremely temperamental when it comes to dot products! For example, if I have the following, ...
1
vote
2answers
86 views

Block diagonal matrix [closed]

Suppose I have 4 matrices: A, B, C, D, and I want to form a block diagonal matrix from these sub-matrices, i.e. it would look like MatrixForm[{{A, B}, {C, D}}] ...
-2
votes
1answer
52 views

Compile Determinant [closed]

I would like to determine the determinant of a 4x4 matrix with the entries a[i,j] being functions of $i$ and $j$. I used Compile with code: ...
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 ...
0
votes
1answer
63 views

Matrix consisting of the matrices [duplicate]

I need Dirac Matrix in my work. They consists of PauliMatrix and ZeroMatrix, which is: ZeroMatrix:=IdentityMatrix[2]-IdentityMatrix[2] I define Dirac Matrix as: ...
3
votes
2answers
108 views
8
votes
11answers
1k views

Ragged Diamonds

diamond[n_Integer] := Table[1, {#}] & /@ (Range[n]~ Join~Range[n - 1, 1, -1]) diamond[5] // MatrixForm How could a more functional, "tablefree", solution ...
0
votes
0answers
49 views

Question about the matrix operation [duplicate]

I was wondering if there is an automatic way to do this kind of matrix operation. For example, for a given matrix ...
1
vote
2answers
159 views
3
votes
2answers
121 views

Inserting rows of one matrix into rows of another matrix sequentially

I have two matrices M1 and M2. Both have same number of columns but different number of rows. I want to make a new matrix M which should have 1st row form M1, second row form M2, third row form M1, ...