# 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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### 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, ...
1k views

### Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
3k views

### Axis/Angle from rotation matrix

With r=RotationMatrix[a,{x,y,z}] I can compute a 3D rotation matrix from axis/angle representation. Given a 3D rotation matrix r...
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### Computing polynomial eigenvalues in Mathematica

MATLAB offers a function polyeig for computing polynomial eigenvalues, which appear, for instance in quadratic eigenvalue problems (see here for some applications) such as: (M\...
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### Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
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 ...
637 views

### Decomposing a matrix with polynomial elements into a polynomial with matrix coefficients

Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}} and I want to ...
1k views

### Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yetâ€¦ Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
1k views

### Higher order SVD

Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6702.pdf but I don't understand their formalism ...
307 views

### How can I compute the representation matrices of a point group under given basis functions?

Take the $C_{3v}$ point group for example: ...
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### Is there any way to obtain an approximate inverse for very large sparse matrices?

I have a very large sparse matrix and I need to obtain its approximate inverse and save it as an sparse matrix too. Any of my efforts as could be seen in what follows fail for large n ...
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### Composition of functions

I have a number of rotations computed by rot = RotationTransform[theta, point], and I would like to compose them to produce one function that is the composition of ...
2k views

### Eigenvalue / Eigenvector Calculation

I'm currently trying to compute the three smallest eigenvectors for a 34 by 34 matrix. While I was expecting this to take some time, Mathematica has been running for the past 3 hours, which seems ...
131 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: ...
3k views

### How do I keep the right ordering of eigenvalues using Eigensystem?

I'm having an issue with the Eigensystem command. I need to diagonalize a bunch of 3 by 3 complex valued matrices, but more importantly, I need to keep the exact ...
1k views

### Can the CholeskyDecomposition function in Mathematica be made to work on non-symmetric matrices?

The CholeskyDecomposition[m] function in Mathematica requires a symmetric and positive definite matrix m. For instance, the ...
835 views