Tagged Questions

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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Tolerance of PositiveSemidefiniteMatrixQ [closed]

I believe the following should be True but returns False for me: ...
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Reliably computing the signature of a matrix with small eigenvalues

When asked to compute the eigenvalues of the following matrix ...
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Nonrectangular tensor encountered [closed]

I am trying to solve a system of equations which characteristic matrix: ...
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How to know the usage of undocumented function like LinearAlgebraBLAS?

BLAS is not documented in mathematica. Using ?LinearAlgebraBLAS* gives But None of the function has a detailed usage information Click any of the ...
117 views

How to solve lowest eigenvalue with Lanczos or Arnoldi algorithm? [closed]

By setting Method->Arnoldi in Eigensystem I was able to solve lowest eigenvalue and eigenstate of a large sparse matrix. ...
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strange timing result of LinearAlgebraBLAS` in mathematica? [closed]

BLAS is short for "Basic Linear Algebra Subprograms". It is a famous collection of routines for doing linear algebra. I just know from Oleksandr R. that mma can directly call BLAS under the context "...
120 views

Hermitian Matrix

From Derbyshire's Prime Obsession, I would like to get the Mathematica code to generate a Hermitian matrix for evaluation and display. $256 \times 256$ would be nice. Random Normal distribution, ...
100 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 ...
74 views

Minimization of linear combination of vectors

Suppose I have a vectors in $\mathbb{R}^{6}$. For example, take the vector $v = k(-2,2,4,6,2,2)$. I would like to find some $k$ with the constraint that the last two components are necessarily non-...
118 views

Efficient solution of huge sparse linear system

I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
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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 $M(x)$ ...
91 views

Count degrees of freedom of a polynomial

I want to count the independent degrees of freedom of a polynomial in three variables $(z_0,z_1,z_2)$. Therefore I take the coefficients of $f$ and compute the rank Jacobian with respect to the ...
182 views

Eigenvector Concern in Large Fractal-Like Matrix (Possible Bug?)

This is my first post and I have quite a long question. Thanks to any who read. To start with, I have an operator m=Transpose[n] on a 7 dimensional vector space V where n is constructed as follows: <...
148 views

How to be more efficient/faster with this MatrixExp-vector multiplication?

I am looking for expertise that helps to improve speed of the code below. First, a little bit of background: There is some system of differential equations $\dot{\vec{m}}(t)=S(t)\vec{m}(t)$. In order ...
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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 ...
55 views

NMinimize error

I want to use NMinimize in the following way: ...
491 views

Sparse Cholesky Decomposition

I am working with square matrices with a special form, which for large rank ($> 100,000$) would be best stored and manipulated as a SparseArray. I believe that ...
155 views

What values of $\delta$ and $\eta$ are being used in LatticeReduce?

The Lenstra–Lenstra–Lovász algorithm has a parameter $\delta$ with $1/4 < \delta < 1$, where roughly speaking the closer $\delta$ is to 1 the longer it takes, but the better basis reduction you ...
410 views

Finding a unitary matrix in Mathematica

I have the following equation : $\tilde{B} = U B U^{\dagger}$ I also know both $B$ and $\tilde{B}$ , I just want to find the matrix U, that gives me the transformation. I tried using ...
128 views

Solving a linear equation in an abstract vector space

I have five abstract vectors a1,a2,a3,a4 and a5 that yield four other objects through abstract addition w1 = a1 + a2; w2 = a2 + a3; w3 = a3 + a4; w4 = a4 + a5; ...
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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 $e_1=\{1,0,0,0\}$, $e_2=\{0,1,0,0\}$... (...
156 views

LU factorization

Basically what I need to do is this: Write an algorithm that finds the LU factorization of the following matrix. The algorithm should perform the necessary elementary row operations to reduce A to U, ...
127 views

Is it possible to find the vectors that span the nullspace of a large, symbolic matrix

My problem is composed of two parts, a large sparse matrix $L$ ($m$x$n$ where $m=10^3$, and $n=10^5$, with $10^7$ non-zero complex numbers), and a dense, symbolic matrix $F$ ($m$x$m$ where $m=10^3$), ...
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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 ...
114 views

Evaluating only one column of a $m \times m$ matrix without evaluating the matrix itself

Suppose I have f[x_] := SparseArray[{someRules}, {m, m}]; g[x_] := MatrixPower[f[x], k]; Would it be possible to evaluate only the $n$-th column ($n\neq m$) of <...
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Solve vs. LinearSolve - ill solutions using both methods [closed]

I'm wishing you a nice day. My question is related to this question previously asked by me, answered by PlatoManiac. Although I found a bug in his post I decided to leave his answer accepted and ask ...
116 views

Eigenvalues FEAST method - performance is very variable

I am running the FEAST method option for Eigenvalues on sparse matrices of dimension around 500,000. I look for about 50 ...
111 views

How to reduce an expression into user-defined variables?

In the following code, I define a set of matrices. Then, I define a function that calculates the commutation relation relation between these matrices ...
60 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. ...
113 views

Find six vectors with rational entries under constraints?

Define six vectors v[i] with i=1,2,3...,6. Each v[i] is six dimensional and all entries in ...