Questions on the manipulation of matrices in Mathematica.

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88
votes
7answers
24k views

Elegant operations on matrix rows and columns

Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ...
28
votes
4answers
3k views

Why does MatrixForm affect calculations?

This is a really newbie question, but it has me confused. Why does this code work without // MatrixForm and doesn't work with ...
63
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 ...
28
votes
5answers
6k views

What is the most efficient way to add rows and columns to a matrix?

Say I have a matrix m and a vector v. ...
5
votes
4answers
13k views

Creating a table/Matrix during a For loop

I have a For loop (with i as a counter), which calculates different values (y1, ...
6
votes
1answer
2k views

Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?

If I ask Mathematica to find the eigenvectors and eigenvalues of the matrix: ...
33
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 ...
21
votes
2answers
4k views

How to enter matrices in block matrix format?

Example: I have a matrix $R = \left( \begin{array}{cc} A & \mathbf{t} \\ 0 & 1 \end{array} \right) $ where $A$ is 3-by-3 and $\mathbf{t}$ is 3 by 1. Or in Mathematica ...
11
votes
2answers
2k views

How to use “Drop” function to drop matrix' rows and columns in an arbitrary way?

The built-in function "Drop" can delete a Matrix's row and column. Typical syntax for "Drop" is as follows: Drop[list,seq1,seq2...] But what if I want to drop a ...
2
votes
1answer
1k views

Contracting with Levi-Civita (totally antisymmetric) tensor

I have an array $v_{ijk}$ which is effectively a rank-$3$ tensor with dimensions $3\times3\times3$, and I need to contract it with $e^{ijk}$, i.e. evaluate $v_{ijk} e^{ijk}$ (see Einstein ...
44
votes
6answers
3k views

Does Mathematica have advanced indexing?

I have two $M \times K$ arrays $L, T$ where I would like to set all the elements in $L$ to zero whenever the corresponding element of $T$ is greater than 15. The ...
9
votes
1answer
415 views

How get eigenvectors without phase jump?

I'm using Eigenvectors to get the eigenvectors for some matrixes, but the eigenvectors seems to have some phase jump. Here is an example: Say we have a 2 by 2 ...
22
votes
2answers
4k views

How to form a block-diagonal Matrix from a list of matrices?

For example, like this: I know join[...] works, but it is a bit troublesome for multiple matrices. I also tried DiagonalMatrix[...], but DiagonalMatrix can only form a matrix from a list of ...
22
votes
3answers
3k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...
7
votes
4answers
573 views

Prepend 0 to sublists

My question is similar to this one, but my goal is to prepend a single 0 the each sublist, not incrementally many 0's. The file I'm working is a CSV containing around 50K sublists of length 35. I've ...
21
votes
2answers
2k views

Cycles of length N in a graph

If I have an undirected graph represented with an adjacency matrix, how can I find all the subgraphs which are a cycle of length N? I don't really know the math nor the programming language well, so ...
37
votes
3answers
1k views

Tiling a square

I wondered if there was a way to automate the process of finding a way to tile a tile into a square. The idea is to represent the tile with a matrix of $0$s for blank space and $1$s for filled spaces ...
12
votes
3answers
4k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
5
votes
2answers
4k views

How to use a 3×3 covariance matrix to plot an error ellipsoid?

I have a 3×3 error covariance in Mathematica, but I don't know how to use it for plotting the error ellipsoid. It would be great if you can show me how I can do that for the below covariance matrix: ...
8
votes
3answers
966 views

How to manipulate gauge theory in Mathematica?

I want to know if there is a way of typing into Mathematica an expression like the following, $$\epsilon^{\mu \nu \lambda} f^{abc} A^a_\mu A^b_\nu A^c_\lambda + g\epsilon^{\mu \nu \lambda} A^a_\mu ...
32
votes
2answers
823 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
3answers
2k views

Correct way to remove matrix columns?

I start off with m = 1000 x 5 matrix, and I would like to remove first column to get 1000 x 4 matrix and repeat again for ...
3
votes
3answers
211 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 ...
18
votes
5answers
705 views

Graph from binary matrix (not adjacency) respecting the original matrix positions

I have a binary matrix. My objective is to connect every close (without "jump") elements with value equal to 1, but I must keep the point positions, just like it's shown at the image. Can somebody ...
8
votes
2answers
873 views

Entering block matrices for an arbitrary matrix size

Background: How to enter matrices in block matrix format? and the following: I want to create $$ f(A,t) = \left [ \begin{matrix} A & t \\ 0 & 1 \end{matrix} \right ] $$ where $A$ ...
5
votes
3answers
2k 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, ...
5
votes
1answer
2k views

Problem with plotting eigenvalues

I want to plot the eigenvalues of a matrix which is dependant on a parameter (well, actually I want to plot a tight-binding electronic band structure). The dimension of the hamitonian matrix is ...
8
votes
1answer
199 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 ...
0
votes
2answers
659 views

Classification of a linear system of equations with a parameter

I need to get every possible value of k that returns infinite number of solutions or no solution to this system: ...
7
votes
1answer
8k 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 ...
12
votes
1answer
280 views

How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area. The function ListSurfacePlot3D creates the surface how I want it. ...
10
votes
2answers
3k views

How to get Matlab data imported with the same dimensions?

I have some Matlab image data with the following dimensions (output is from Matlab): >> size(im) ans = 86 86 3 45 The data imports just fine ...
10
votes
1answer
293 views

Drop selection of columns from a ragged array

I have an application where I need to drop some arbitrary list of columns from a ragged array (where of course the shortest array rows have at least all the specified columns). E.g., given a ragged ...
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 ...
14
votes
6answers
726 views

How to find the distance of two lists?

I have two lists as the followings: ab = {1, -1, -1, -1, 1, 1}; ac = {1, -1, -1, 1, 1, 1}; How I can find the difference (more precisely, the edit distance) ...
14
votes
3answers
1k views

Constructing a symbolic Hermitian matrix

I need to construct a symbolic Hermitian matrix like m = { { n, a, b, b}, {Conjugate[a], n, b, b}, ... } but I am not able to set ...
12
votes
1answer
264 views

Why does partitioning increase Dot execution speed?

I have noticed that multiplying a list of matrices can be significantly sped up by partitioning the list, calculating the product of the partitions matrices, and then multiplying the results. ...
10
votes
1answer
862 views

Nesting Parallel processes

I just attempted to run code that had nested ParallelMap[] functions. It generates the error message: ParallelMap::subpar: Parallel computations cannot be nested; proceeding with sequential ...
3
votes
2answers
733 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 ...
10
votes
2answers
1k views

Non-commutative symbolic linear algebra

I am fairly new to Mathematica but I thought I would be a helpful tool to carry out a few simple linear algebra calculations. It seems like an easy task but I cannot figure out how to do it. For ...
0
votes
2answers
180 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 ...
4
votes
3answers
376 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 ...
2
votes
1answer
502 views

Why is EigenValues returning Root expressions?

This is the code I have: ...
1
vote
2answers
175 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 = ...
16
votes
5answers
3k views

Best way to create symmetric matrices

From time to time I need to generate symmetric matrices with relatively expensive cost of element evaluation. Most frequently these are Gram matrices where elements are $L_2$ dot products. Here are ...
14
votes
4answers
1k views

What is the fastest way to locate an image inside a larger image?

let b = let c = How to do: find[c,b] that returns the bounding box of c in b? ...
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
391 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 = ...
14
votes
3answers
614 views

Why is calling Dot with many arguments so inefficient?

Say I want to multiply a reasonably large list of symbolic matrices. ...
10
votes
5answers
1k 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 ...