Questions on the linear algebra functionality of Mathematica.
11
votes
1answer
329 views
What is the fastest way to find an integer-valued row echelon form for a matrix with integer entries?
Let me begin by saying that this is my first post on StackExchange. I apologize in advance if I unwittingly break any of its unwritten rules of etiquette.
Recently, I've been trying to understand an ...
6
votes
0answers
228 views
Inverse of a large sparse Hermitian block matrix
I am looking for a method (if it exists) for the inverse of a large sparse Hermitian block matrix.
The off diagonal sparse matrices, named δ are 4x4, and they have ...
16
votes
3answers
1k views
How to symbolically do matrix “Block Inversion”?
Consider a block (partitioned) matrix
matrix = ArrayFlatten[{{a, b}, {c, d}}]
where, a, ...
0
votes
1answer
240 views
On the parallelization of matrix multiplications in Mathematica 8
I have installed Mathematica 8, but I think the commands for parallelizations do not work! Even when I try to test the example in the Help of Mathematica, I face with
ParallelDo::nopar: No ...
6
votes
1answer
339 views
Higher order SVD
Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://csmr.ca.sandia.gov/~tgkolda/pubs/bibtgkfiles/TensorReview.pdf but I don't understand their ...
3
votes
2answers
346 views
Solving a linear equation in Mathematica
This should be easy but I can't seem to find the right way to do it.
I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters ...
2
votes
3answers
572 views
Orthonormalization of non-hermitian matrix eigenvectors
When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
6
votes
2answers
371 views
Entering block matrices for an arbitrary matrix size
Background: How to enter matrices in block matrix format? and the following:
I want to create
$$
f(A,t) = \left [
\begin{matrix}
A & t \\
0 & 1
\end{matrix} \right ]
$$
where $A$ ...
4
votes
3answers
463 views
Trying to simplify Root expressions from the output of Eigenvalues
I am trying to calculate eigenvalues of a sparse matrix with only two distinct non-zero elements, here Alpha and Beta, which are both negative reals. Mathematica returns some complex expressions with ...
1
vote
0answers
240 views
Matrix multiplication involving MatrixForm [duplicate]
Possible Duplicate:
Why does MatrixForm affect calculations?
I am doing a matrix multiplication, but not getting the desired output. I am doing the matrix multiplication of $A^{-1}B$ from ...
4
votes
2answers
258 views
ordering of functional eigenvalues
Is there any order to the symbolic eigenvalues of a matrix returned by the command Eigenvalues[...]?
While numerical eigenvalues are listed in descending order ...
7
votes
3answers
279 views
Composition of TransformationFunctions
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 ...
4
votes
1answer
176 views
Obtaining a thin/compact SVD
I'm using SingularValueDecomposition for a least-squares regression, the instruction that works fine for what I need is
...
5
votes
1answer
789 views
Simpler way of performing Gaussian Elimination?
Is there a simpler way of performing Gaussian Elimination other than using RowReduce? Such as a single built in function?
Edit: Look at the example from our simulation class. Not too difficult, but ...
5
votes
4answers
1k views
Computing eigenvectors and eigenvalues
I have a (non-sparse) $9 \times 9$ matrix and I wish to obtain its eigenvalues and eigenvectors. Of course, the eigenvalues can be quite a pain as we will probably not be able to find the zeros of its ...
9
votes
3answers
431 views
Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering?
If I do back to back calls of Eigenvalues[] and Eigenvectors[] can these be assumed to order the values and vectors the same, or ...
3
votes
1answer
512 views
Obtaining the square-root of a general positive definite matrix
I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., ...
4
votes
1answer
229 views
How to fix errors in Gram-Schmidt process when using random vectors?
I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
8
votes
1answer
233 views
Why is MainEvaluate being used when LinearSolve can be compiled?
According to this question LinearSolve can be Compiled. However, CompilePrint shows a MainEvaluate but no-warning is generated. It appears that LinearSolve is not ...
4
votes
0answers
155 views
NullSpace[_, Method->“OneStepRowReduction”] is sometimes wrong; how can I work out when this happens?
(This is on MMA 7.0.1.0 on OS X)
I've just found a large matrix m for which NullSpace[m] and ...
14
votes
2answers
972 views
How to enter matrices in block matrix format?
Example:
I have a matrix $R = \left( \begin{array}{cc}
A & \mathbf{t} \\
0 & 1 \end{array} \right) $ where $A$ is 3-by-3 and $\mathbf{t}$ is 3 by 1. Or in Mathematica
...
