Questions about Mathematica functionality related to manipulating vector spaces and linear mappings between such spaces. This includes determination of matrix properties, matrix transformations, decompositions, and factoring.

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1answer
99 views

How can we use RowReduce with a modulous AND variables?

We can use RowReduce with a field. For example, we state RowReduce[{{1,3,5},{0,1,2}},Modulous->23] ...which then returns: ...
2
votes
4answers
449 views

Selecting terms containing some expression

Imagine I have an expression like a*k + (a^2)*b*c + b*e and I would like to obtain the term containing, for example, some power of a. In that case I would ...
2
votes
3answers
282 views

Adding elements in the sublists

How can I add the elements in the sublists? For example, if I have the list which is m={{1,3},{2,3},{4,1}} then, the output that I want is ...
2
votes
1answer
74 views

Expand a product of operators

Lets suppose I have a family of operators $f_i$, and unknown c-numbers $a,b,c$. I want to expand such products: $(f_1+f_2+c)(f_3+f_2+b)$ into $b c+b f_2+b f_1+c f_2+c f_3+f_2^2+f_1 f_2+f_2 f_3+f_1 ...
2
votes
1answer
63 views

Algebraic Manipulations with Indices

I am absolutely new to Mathematica, but I've heard it is a pretty powerful tool for symbolic calculations. My problem (stated generally): I have three dimensional array. I define a symbolic operator ...
2
votes
1answer
95 views

Row echelon form question

I am wondering if there is a Mathematica command that will put a matrix in row echelon form. That is, put $$ \begin{bmatrix} 1 & 2 & 3\\ 2 & 3 & 4\\ -1 & 0 & 2 \end{bmatrix} ...
2
votes
1answer
68 views

Inverting matrix with assumptions

I want to invert a matrix that contains some variables, so I thought I should give some assumptions to Mathematica to speed up the process. How do I assume that $s0,...,s8$ are positive constants ...
2
votes
1answer
117 views

Maximizing the number of zero entries in a matrix

I have a matrix with a bunch of parameters in its entries, they all come in different combinations in different places of the matrix. I can post the matrix itself if requested, but I think what I mean ...
2
votes
1answer
114 views

Anyone knows the algorithm used by NullSpace function?

NullSpace function gives a list of vectors that forms a basis for the null space of the input matrix. When the rank of the input argument matrix $M_{m\times n}$ is ...
2
votes
1answer
38 views

Linear function on strings using UpValues

I have two functions Sup and Sdown that take a string of letters with allowed characters ...
2
votes
1answer
170 views

Problem with Eigenvectors when given a matrix containing approximate numbers and symbols

I'm trying to diagonalize a certain 2 x 2 matrix, but Mathematica refuses to find the eigenvectors. In particular, when I input ...
2
votes
1answer
249 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 ...
2
votes
1answer
493 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
0answers
45 views

Explicitly find a guaranteed factorization of large expression?

Consider the large expression LE defined in this file (involving only linearly independent functions), or in this file (linear interdependence present but slightly ...
2
votes
0answers
74 views

Suggestions for solving a large linear system

I have a system of $\approx 200,000$ linear equations in $\approx 40,000$ variables (with rational coefficients) and I would like to determine the dimension of the solution space, which I know to be ...
2
votes
0answers
57 views

Derivative of vector dot product with respect to a vector

I have the expression: Transpose[gvecI, {2, 1}].x (m[1] + m[2]) gvecI and x are [3x1] ...
2
votes
0answers
50 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
2
votes
0answers
41 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
2
votes
0answers
62 views

MatrixRank of a large but sparse matrix

I want to find the rank of a very sparse, quite rectangular matrix mat, but I'm running out of RAM (I have 16 GB) if I try to use ...
2
votes
0answers
32 views

How to get simultaneous eigenvectors of commuting matrices? [duplicate]

So let's say there are two square matrices A and B that commute (AB-BA=0). This implies that there must exist some complete set of vectors that are eigenvectors of both A and B. Is there any way to ...
2
votes
0answers
75 views

Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
2
votes
0answers
22 views

What is the most efficient method to find a single eigenvector with eigenvalue that is numerically 0?

I need to find an eigenvector of a (numerically calculated) square matrix M corresponding to the eigenvalue 0. The methods I know are ...
2
votes
0answers
91 views

How to make Eigensystem in version 10 produce the same results as version 9 [duplicate]

The Eigensystem in version 10 seems to give slightly different results as in version 9: ...
2
votes
1answer
896 views

How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
2
votes
0answers
200 views

Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)

I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
1
vote
3answers
216 views

Using mathematica to visualise solution of vectors and planes

Im struggling with a question I'm my math book and I wanted to use mathematica to visualise it for me, the problem is that I don't even get something remotely similar to what I was expecting. How here ...
1
vote
2answers
256 views

Computing distance matrix for a list

Using functional programming in Mathematica, how can I compute a distance matrix for every element in a list of matrices... The distance would be computed between the item in the list and a "target ...
1
vote
2answers
324 views

What's the best way to generate all the upper triangular matrix whose singular values are given?

For example, given $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 3$, what's the best way to generate all the upper triangular matrix ($3\times 3$) whose singular values are $\lambda_i$? Note:Given a ...
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
1answer
160 views

Efficient algorithm to generate a basis for exact diagonalization

The problem is described as follows: I need to generate a basis(matrix) in lexicographic order. For two different basis vector $\{n_1,n_2,\cdots,n_M\}$ and $\{t_1,t_2,\cdots,t_M\}$, there must exist ...
1
vote
2answers
71 views

Create a random 2×2 matrix with a repeated eigenvalue and single eigenvector

Does anyone have a good technique for creating a random $2\times 2$ matrix that has one eigenvalue of multiplicity two, but only a single eigenvector? And more generally, has anyone written a ...
1
vote
1answer
712 views

Is LinearSolve the most robust way to solve the equation $Ax=b$?

I want to solve the equation $Ax=b$, where $A$ is an $n\times n$ matrix, and $x$ and $b$ are $n\times 1$ column vectors. Here $n=124$. LinearSolve[A,b] I got the ...
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2answers
141 views

Solve a symbolic underdetermined Linear System

Dear StackExchange Community, I'm trying to solve an indeterminate linear system of equations, with $n+1$ variables and $n$ equations; therefore, I need to express all $n$ other variables a function ...
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2answers
98 views

How to extract matrix which produces given symbolic linear combinations?

Suppose I have a column matrix $\alpha$, consisting of some symbols ...
1
vote
2answers
179 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 = ...
1
vote
1answer
629 views

How to simulate the response of a linear parametric varying system in Mathematica?

Consider the following system \begin{align} \dot{x}(t)&=\sum_{i=1}^{2}\rho_{i}(x(t))\left[A_{i}x(t)+B_{i}u(t)\right]\\ y(t)&=Cx(t) \end{align} with: ...
1
vote
1answer
74 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 ...
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vote
1answer
90 views

Matrix multiplication for higher dimensional matrices [duplicate]

I have a matrix like this (myb1): I would like to get the matrix multiplication of each of the submatrix to itself. For example the first 2x2 matrix $\begin{bmatrix}1 & 2\\1 & ...
1
vote
1answer
149 views

Transform linear system into a matrix form

I have a system of linear equations in variables $A_n$ of form: $$ \sum _{k=-K}^K h_k A_{n-k} J_{n-k}\left(\frac{(1-i) \text{$\eta $Sqrt}(n-k)}{\sqrt{2}}\right)+A_n\left(\frac{(1-i) \eta ...
1
vote
1answer
149 views

Why can't Mathematica compute the null space of these matrices?

I'm writing a library of functions to work with musical pitch-class vectors. One of my functions gives me a skew-symmetric matrix modulo 12 that corresponds to the differences between components of ...
1
vote
1answer
141 views

How smart is Solve? Figuring out what tricks I should try

I'm trying to solve a large system (~10000) of linear equations using Solve, but the process keeps failing. As-is, I don't know whether it's failing because it's using too much memory or too much time ...
1
vote
1answer
238 views

LinearSolve failing to find solution to system of linear equations of 64 variables

I've got a 64x64 Matrix L for which I want to find the solution to the matrix equation L . x == rho. L is defined as ...
1
vote
1answer
302 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 ...
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vote
1answer
214 views

Hermite Normal Form in “columns” convention

After describing the Hermite Normal Form (HNF), MathWorld explains: The Hermite normal form for integer matrices is implemented in Mathematica as ...
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1answer
677 views

Is Mathematica matrix multiplication with its inverse wrong? [duplicate]

Possible Duplicate: Why don't * and ^ work as I expected on matrices? When I enter this ...
1
vote
1answer
64 views

Multiplying three matrices does not give expected form [closed]

I'm having lectures on analytic geometry. I've learned that there is an associated matrix multiplication for a quadratic form: $\quad \quad \left( \begin{array}{ccc} x & y & 1 \\ \end{array} ...
1
vote
1answer
84 views

Efficient calculation of diagonal matrix elements

I have a matrix $V$ of size $M$ in which each row $i$ is a vector $v_i$. Now I have another matrix $H$ and I would like to calculate as efficiently as possible the list of values $v_i^\dagger\cdot ...
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1answer
129 views

Transform list of inequalities into matrix form $A\ x \leq b$

I have a list of linear inequalities, and I want to get it into the form $A\ x \leq b$; i.e., find the matrix $A$ and the vector $b$. Is there any function in Mathematica that can that can do this?
1
vote
1answer
55 views

Mathematica computes wrong eigenvectors? [closed]

I have a matrix M = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, b}, {0, 0, -b, 0}} that I want to diagonalize. So far, I always used the following and it worked, but ...