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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Why is KroneckerProduct(vector,vector) a matrix in mathematica, not a vector?

"If A is an m × n matrix and B is a p × q matrix, then the Kronecker product A ⊗ B is the mp × nq block matrix" from Wiki Thus the Kronecker product of two vectors, i.e. $3\times 1$ matrices, ...
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95 views

Orthogonalization is not commutative!

I get stuck into a problem: I am going to produce orthogonalized eigenvectors of a matrix and in any iteration. I shortened my question in the bellow line: Why do we face to different results of ...
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1answer
120 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} ...
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1answer
75 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 ...
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106 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...
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136 views

Efficient method of raising matrix to a variable power?

I have a $2 \times 2$ matrix $A$, where each element is a 12th order polynomial in a parameter $a$. I need to raise this matrix $A$ to the $-t/T$ power, where $T$ is a known scalar (for this ...
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151 views

Why does LyapunovSolve solve non-standard form?

LyapunovSolve[A,Q] solves the equation $A P + P A^T = Q$ for $P$ whereas the standard form (wikipedia,lecture notes, p.25, linear control systems) of the Lyapunov ...
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89 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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52 views

A bijection between a list of $n$ elements and the canonical basis of $\mathbb{R}^n$

I have some lists omega[i], i=0,1,...,15. And, e.g., omega[0] has four elements. I would like to define a function that maps omega[0][[i]] into $e_i$, where $e_1=\{1,0,0,0\}$, $e_2=\{0,1,0,0\}$... ...
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152 views

Linearity of a function in Mathematica

I have a function which has something like myFunc[q,a state[c,d]] a could be anything, and I want to tell Mathematica that ...
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2answers
141 views

How to extend “List-of-numbers-with-number” arithmetic to “List-of-X-with-X” arithmetic? [duplicate]

I'll start with a couple of examples (since this is all one can get from the documentation anyway). First, adding lists of numbers equal length is done term-by-term. E.g. ...
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103 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 ...
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758 views

Matrix echelon/upper diagonal form

Is there a way to find the echelon form of a matrix in Mathematica? I see there is a function to find the reduced echelon form, RowReduce[], but I can't see ...
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864 views

Calculating an exact orthogonal modal matrix in Mathematica

I can calculate the modal matrix of a matrix A using the command JordanDecomposition[A][[1]], and a decimal approximation of the orthogonal (or normalised) modal ...
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2answers
1k views

How to Solve or LinearSolve $A = I$ matrix equation?

I'd like to solve this equation for $A = B$ where $B = I$, which represents 3 systems of 3 linear equations, for $a, b, c, d, e, f$, without writing LinearSolve 3 ...
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32 views

How to find selected elements of inverse of a banded matrix without inverting it?

Is it possible to find some selected elements of the inverse of a large sparse matrix without inverting it? For example consider this Hermitian matrix (as a general case). ...
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91 views

Finding matrix given null space

Suppose I input a very large $n$ integer vectors and I wish to compute the matrix whose nullspace is spanned uniquely by these vectors. Is there an appropriate command/module to do this using ...
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44 views

NMinimize error

I want to use NMinimize in the following way: ...
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2answers
126 views

LUDecomposition for non-square matrices

How do we go about finding the LUDecomposition for non-square matrices. When i try to input the standard LUDecomposition ...
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88 views

Transposition of state space form of a transfer function

How can I transpose the output of state space model in Mathematica? trying the following code would transpose the top right symbol s instead of the matrices. ...
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1answer
88 views

Handle matrices and vectors with general dimension

I have a matrix of $n \times n$ dimension: $$ K - \omega^2 M = \begin{pmatrix} 2\omega_0^2 - \omega^2 & - \omega_0^2 & 0 & \cdots & 0 \\ - \omega_0^2 & 2\omega_0^2 - \omega^2 ...
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121 views

Extract coefficient matrix $A$ from expression $f(x)$

I have expression: $$f(x)=\sum_{i=0}^{K-1}\sum_{j=0}^{N-1}a_{i,j}e^{ix}x^j.$$ I want to extract coefficient matrix $A$ from expression $f(x)$ where $$A=\left( \begin{array}{ccccc} a_{0,0}& ...
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134 views

Are variables always assumed to be real in Jordan Decomposition?

If you give the following input in Mathematica 9.0 (Student Edition): JordanDecomposition /@ ({{1, #}, {#, -1}} & /@ {i, I}) Mathematica gives you two ...
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70 views

Eigenvectors with imaginary part

I am working on the following: ...
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176 views

Forcing solutions to avoid Root[]

I'm solving a system of ordinary non-homogeneous differential equations (4 equations). The solutions will include some algebraic equations solutions as known from text books due to the use of an eigen ...
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49 views

Minimization problem in a subset of Complex matrices

I would like to minimize $||\mathbf{A} \rho -v||$ (where $\rho , v$ are fixed vectors) with respect to the matrix $\mathbf{A}$ elements, but with $\mathbf{A}$ in a subset of complex matrices (i.e. ...
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203 views

Basis for the intersection of vector spaces

The MuPAD Notebook Interface provides the linalg::intBasis function: http://www.mathworks.com/help/symbolic/mupad_ref/linalg-intbasis.html How can I get the same ...
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74 views

How to rearrange CharacteristicPolynomial[ ] terms?

I have a symbolic matrix A, which I need to find the characteristic polynomial, then order the polynomial in greatest-to-least form. (Ultimately to find the matrix inversion via Cayley-Hamilton ...
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2answers
120 views

Using conditionals to check if LinearSolve found a solution

Is there some way to check if LinearSolve found a solution using conditionals in Mathematica 9? I need to solve a large number of linear equations, but I am only interested in the cases where there ...
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1answer
52 views

Correctly substituting a matrix into a scalar equation [duplicate]

I am having trouble correctly substituting a matrix into an (originally) scalar equation. For example: A = {{3, 1}, {1, 2}} cp = CharacteristicPolynomial[A, x] ...
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201 views

What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
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1answer
104 views

Why TensorReduce not working here?

I would like to use TensorReduce to work on the tensor contraction $y_{ib}y_{ia}$ (where index $i$ is summed). However, ...
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2answers
790 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: ...
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374 views

Partial row reduction of a matrix

I have an $m\times n$ matrix (presumably of full rank) with $m>n$, and I would like to row reduce it, but leave the last column unreduced; that is, I want to get output on the form $\pmatrix{ 1 ...
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1k views

Using singular value decomposition for graph clustering

I have a fairly large graph (50-60 vertices) with directed, weighted edges, and I am attempting to cluster the vertices. Prior to this, I have only worked with undirected graphs having symmetric ...
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1answer
41 views

Array Flattening arrays of matrices given by rules

Fix an $n$ and an $m$ positive integers.I have some set of four $n\times n$ matrices $A$,$B$,$Y$,$Z$ (where $Z$ is the zero matrix). I'd like to input the $nm\times nm$ matrix of block matrices given ...
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1answer
74 views

How to plot the field of values of a matrix

For a given matrix A (let's say of dimension 2 to keep it simple), I need to plot in the complex plane its field of values. The field of values of a matrix is defined as the set $\{\langle{Ax, ...
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2answers
126 views

Is this caused by round-off errors?

Let's consider this integration Integrate[ E^(4 n x s) (1 - x)^(-1 + 4 n μ) x^(-1 + 4 n ν), {x, 0, 1}] It returns ...
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207 views

Solving a System/Matrix of Equations in Matrix Form

Ok, I am trying to solve an equation involving matrices (well, tensors actually), which is of the form: $\mathbf{e}^{T} \cdot \mathbf{M} \cdot \mathbf{e}$ = $\mathbf{N}$, where $\mathbf{e}$ is an ...
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1answer
121 views

Simplification of linear algebra [duplicate]

I have a few vectors defined as V1 = Array[v1,3] V2 = Array[v2,3] V3 = Array[v3,3] And I am trying to solve a very simple equation along the lines of ...
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1answer
236 views

What is most efficient way to convert system of equations to collection of functions?

I have the type of system M.x = b, where M is a known matrix and b is a known vector. M contains many parameters, call the entire parameter set 'a', so M => M[a]. I want to be able to efficiently ...
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167 views

Solve equations for all values of variables, rejecting certain types of solution

I have an expression, expr, containing 3 variables, 4 coefficients and 2 non-zero generic constants. I want to solve for the 4 coefficients such that the equation ...
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1answer
121 views

Using Dot Product with InterpolatingFunctions

I am using NDSolve on a vector function $\mathbf y'(x)=f[\mathbf y(x)]$ with initial condition $\mathbf y_0$, where the dimension of the vector should be user-defined. ...
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0answers
57 views

Deriving ordinary least squares (OLS) in matrix form

How can I instruct Mathematica to derive the OLS in matrix form with respect to $\beta$ and obtain the result ${-2X}^{T}(y-X\beta)$? The matrices have the following dimensions: $y_{n \times 1}$, ...
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0answers
47 views

Mapping over two indices with a condition

How can I use Map over two indices with a condition? I am trying to calculate second derivative of an eigenvalue, $\lambda_i(x)$, of $n \times n$ matrix $M(x)$ ...
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55 views

Multivariate Path Construction using Sobol numbers

I am sharing my code,which I have tried to perform as per the instruction mentioned below. Please correct it so that I could get my output. Instruction: Use the first m dimensions of the Sobol vector ...
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0answers
63 views

“Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
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0answers
44 views

Rotating an oriented surface in 3D

I have an oriented surface S in three dimensions. Let's say that initially the surface is parallel to the x-y-plane with orientation vector ...
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0answers
55 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
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111 views

MatrixExp of a complex matrix of size about 10000 by 10000 [closed]

I want to apply MatrixExp of a numerical, complex matrix of size about 10000 by 10000, and I also need high precision as I need to multiply several such matrices. ...