# 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.

113 views

### Solving large linear systems of equations efficiently?

I need to solve linear systems of equations of approximate size $(n!)\times(n!)$ as efficiently as possible for as high parameter n as possible. All the entries ...
180 views

### Finding eigenvalues in Mathematica: why so slow?

I am trying to find the eigensystem of a large sparse real symmetric matrix, and I only need the lowest 40 or so eigenstates. The relevant code is as follows: ...
98 views

### diagonalization function

If we have a matrix m which is n*n, how can I do mm=U^dagger m U which is a transformation ...
139 views

### Why has Version 10.3 precision reduced?

In version 7.0.1.0 and versions 10.0 and 10.1 the following is produced: ...
46 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). ...
69 views

### LinearSolve on non-square matrices?

I just came across a strange behaviour for LinearSolve (on Mathematica 8.0.0.0). Consider the following definitions: ...
80 views

154 views

### Write Sum of Matrices Explicitly

I have sum of lots of matrices A+B+C+D+E+... and I want that Mathematica shows me this as explicit matrix sum, i.e. Explicit Matrix A + Explicit Matrix B + Explicit Matrix C + .... and not just ...
34 views

### TensorContract with KroneckerProduct instead of ordinary Times

Is it possible somehow to contract two tensors, say A={{a1,a2,a3},{a4,a5,a6}} and B={b1,b2,b3}, where the elements ...
127 views

### Explicit Contraction of Tensor Indices [duplicate]

Is there any easy way to explicitly contract indices of several given tensors. For example, ...
1k views

### Generating random symmetric matrix

Suppose first that I want to generate a matrix whose elements are independent and identically distributed (i.i.d.) with distribution dist. This is easy: ...
610 views

### more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559 + 1.682941969615793 I}, {2.161209223472559 - 1.682941969615793 I, 2}} and ...
135 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 command,...
228 views

### How write a new MatrixRank feature with symbolic computation

The current MatrixRank is a slight foolish without any capacity of symbolic computation ,feature of Mathematica, like this: <...
42 views

### Tolerance of PositiveSemidefiniteMatrixQ [closed]

I believe the following should be True but returns False for me: ...
139 views

### Generate random Hermitian matrices [duplicate]

I want to generate random Hermitian matrices. For now, random Hermitian matrices with size 2 are obvious to construct. But elegant methods for higher dimension would be nice! Are there methods besides ...
34 views

### Handling a matrix with components greater than machine precision

I have four quantities stemming from a 4th order differential equation. I can represent these as a vector which is a product of a 4X4 matrix  M=\left\{v,\frac{\partial v}{\partial x},\frac{\partial ...
79 views

### CharacteristicPolynomial returns 0

I have a following matrix. ...
62 views

### Eigenvalues are not the same in the special case

I have this matrix: h = { {e1, 2, x}, {2, 2, x}, {x, x, 2} }; I want to calculate the eigenvalues and then set x equal to zero: ...
145 views

### What is the correct way to perform the Gram-Schmidt process?

Im trying to do a simple processing in Mathematica. My original code was in Matlab. Part of the computation is Gram-Schmidt process, which is an iterative calculation. Every vector is changed ...
82 views

### How can I calculate $(y - A \,x)^{T}(y -A\,x)$ symbolically? [closed]

Given that $x$ and $y$ are column vectors and $A$ is a matrix, I figured out the result $y^{T}y-2y^{T}Ax +x^{T}A^{T}A\,x$ I want to use Mathematica to make such calculations. how do I enter them into ...
BLAS is not documented in mathematica. Using ?LinearAlgebraBLAS* gives But None of the function has a detailed usage information Click any of the ...