Questions on the manipulation of matrices in Mathematica.

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2
votes
3answers
801 views

Convert coefficients of polynomials into a matrix

I have several sets of 5 polynomials of the form: ...
5
votes
1answer
920 views

Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
9
votes
2answers
885 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 ...
14
votes
3answers
5k views

Solving a time-dependent Schrödinger equation

I want to solve the time-dependent Schrödinger 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 that ...
1
vote
1answer
104 views

Is there a cleaner/shorter way to select-replace in matrices? [duplicate]

I love Mathematica, but I find it oddly lacking when it comes to how matrices are handled. Here is an example of code that works but seems like it should be a lot shorter (and minus the loop). I'm ...
8
votes
2answers
506 views

Why does my matrix lose rank?

I want to check the rank of a matrix for observability, but Mathematica loses a rank if the matrix contains very large numbers. Let's say my matrix is ...
5
votes
2answers
6k 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: <...
2
votes
1answer
697 views

Why is EigenValues returning Root expressions?

This is the code I have: ...
2
votes
1answer
346 views

Replace a specified portion of an array with elements from another smaller array

This may be a trivial question, but I have been at it for a couple of hours and I have not made much progress. I have a 10 x 10 array (T) that I have used to generate an 8 x 8 array (Q). I want to ...
0
votes
1answer
100 views

Why does Eigenvalues[matrix I defined] not work? [duplicate]

This is the code I have in my mathematica notebook. I want to find the eigenvalues of the matrix I created called Hmatrix as defined below. However when I type Eigenvalues[Hmatrix] I get the Hmatrix ...
2
votes
1answer
660 views

How to use Compile for accelerating matrix multiplications?

I am trying to find the inverse of the matrix $A$ m = n = 500; SeedRandom[123456]; A = RandomReal[10, {m, n}]; iteratively using the following matrix ...
3
votes
1answer
675 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 ...
-1
votes
1answer
167 views

An issue regarding Eigenvalues function [closed]

Can anybody please kindly explain to me why the members of the output vector produced by the following example are not equal to zero? ...
1
vote
1answer
2k views

Importing a matrix from a text file

I have a $4 \times N$ matrix in a .txt file of the form: -17.071 137.567 16.554 0.65 -16.873 136.138 16.934 0.7 -15.397 135.738 16.894 0.7 -14.7 135.982 15.9 0.6 ...
1
vote
3answers
2k views

How do I create a matrix of functions?

I'm trying to create a matrix in which the elements are functions of two variables, but I can't figure out how to do it. Is it possible? The only way I could figure out is to define the matrix in ...
2
votes
1answer
533 views

Solving an equation involving a determinant

I have a matrix which doesn't include numerical values. There are four variables in it. It is defined by ...
3
votes
2answers
933 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
3answers
453 views

Permanent minors

The function Minors yields the minors of a matrix. Is there a function that yields the permanent minors of a matrix?
12
votes
1answer
2k views

Eigenvalues and Determinant of a large matrix

Can anybody kindly explain to me what is going wrong regarding a simple problem I have? I can find the eigenvalues of a large matrix using Eigenvalues[], but when I ...
1
vote
1answer
82 views

Confirming the existence of a function related to a matrix

Is it possible to get an answer to the following question in Mathematica? Let $M$ be a $n$ by $n$ matrix, is there a function $m:\mathbb{N}\times \mathbb{N}\rightarrow \mathbb{Z}$ such that $m_{ij}=...
7
votes
1answer
626 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 ...
14
votes
2answers
3k 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 ...
4
votes
0answers
180 views

How to accelerate updating some parts of sparse matrices?

I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use ...
6
votes
1answer
178 views

How to calculate only four elements per column in a block matrix?

I have a matrix generated like this : Table[Sequence @@ {f[t[[i]], j, x], g[t[[i]], j, x]}, {i, 16}, {j, 3}] where $f$ and $g$ are two different functions, $t$ ...
8
votes
3answers
756 views

Multiply a list of matrices by a list of vectors

How does one multiply a list of matrices by a list of vectors, elementwise? For example, multiplying ...
1
vote
1answer
594 views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
8
votes
1answer
288 views

inverse of abstract matrix

If you assume the matrix $A$ is invertible, then $A^{-1} \cdot A = I$. Is there an assumption for invertibility in Mathematica 9? How can one make the following evaluate to the identity matrix $I_3$? ...
10
votes
2answers
441 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 I'...
26
votes
2answers
6k 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 ...
3
votes
3answers
274 views

How to transform and swap columns of this matrix in a simple way? Version 2

So, earlier today I asked the question How to transform this matrix & swap its columns in a simple way? and was given useful and elaborated answers. Now, I'm still not used to the "Array", "...
0
votes
2answers
1k views

How to get complement from two matrices?

This is a special case of my question How to do nor on matrices? ...
3
votes
4answers
512 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{...
0
votes
1answer
167 views

How to do nor on matrices?

Supose I have matrices a b and c like a = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; b = {7, 8, 9}; c = {{1},{4},{7}}; I want to get ...
12
votes
2answers
4k views

Badly conditioned matrix (General::luc)

With some matrices, I am receiving the following message: ...
11
votes
1answer
10k 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 ...
2
votes
1answer
281 views

Can I reduce a matrix inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$?

I'm new to Mathematica. When I do linear algebra, I wonder if I can have an inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$, where $\mathbf x$ is a column vector ...
0
votes
1answer
182 views

Discrete 3D plots of median ratios of two 2D matrices of lists of values

Lets say I have 2 2D arrays where each cell contains a list of values: Example: ...
0
votes
0answers
49 views

Inverting a matrix [duplicate]

Possible Duplicate: Why does MatrixForm affect calculations? I am facing a strange behaviour from Mathematica when asking it to invert the following matrix: ...
3
votes
1answer
353 views

Efficiently finding the maximum value of a column in a matrix

Imagine I have a matrix of the following form: TestArray = $((a_1,b_1,...),(a_2,b_2,...),(a_3,b_3,...),...)$, where a specific example might be: TestArray = $((10^6,1,...),(10^7,7,...),(10^3,4,...))...
1
vote
3answers
781 views

More than one expression in the Table[] command?

I would like to construct a Matrix using the Table[] command. The issue is that I would like to use more than one expression for it. What I need to obtain is something like this : ...
5
votes
1answer
335 views

How to define and compute various properties of a variable size matrix

I have a rather simple question, but I have not been able to figure out how to implement a solution in Mathematica. I would like to define a variable size square matrix, say an N x N matrix A, whose ...
2
votes
2answers
239 views

How can I shift the frame ticks to the corner of each element-cell in a Matrixplot?

I am using the following code,to create a Legend for my plot. I would like to shift (or re-position) the frameticks to the corner of each of the cell-elements instead of being in their middle. I ...
0
votes
0answers
76 views

Trying to access element of a matrix [duplicate]

Possible Duplicate: Question about MapThread and Dynamic I'm trying to extract element of a matrix. Let's suppose that the matrix is ...
3
votes
2answers
382 views

Dynamic matrix multiplication

I have the following problem: I want to multiply two matrices and sum them to another matrix C. A.B+ 2B Easy! The matrix A varies as a function of three inputs a,b and c. The second matrix, B, is a ...
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
2answers
289 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: ...
1
vote
1answer
119 views

How can I find the row differences of a matrix?

How can I compute the row differences of an m x n matrix to obtain an m-1 x n matrix; that is, given how do I obtain
0
votes
3answers
720 views

How can I fill in a matrix at every iteration of a Do loop?

I have a matrix whose dimensions are 26x26x3. For my assignment I have written a program which is using a Do loop (maxx=maxy=10,maxz=2): ...
3
votes
3answers
368 views

Correct way to populate a DiagonalMatrix?

I would like to create a series of correlation matrices that starts with : sensMat[[1]] = DiagonalMatrix[ { 1,1,1,1,1 } ]) // MatrixForm and iterates in 0.1 ...
6
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 ...