# Tagged Questions

Questions on the various algorithms used in linear algebra computations (matrix computations).

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### Fast way to find a matrix with only $0$ and $1$ as entries full-rank or not?

I have a huge number of small Zero-One Matrices($4\times 4$, $5\times5$,$6\times6$) and I want to determine whether they are full-rank or not one by one. Gaussian elimination is a option, I want to ...
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### Matrix in Matlab

I'd like to compute the centralizer of a subgroup $H$ of orthogonal group $O(8, R)$, so I need to solve the equation $AX=XA, BX=XB \mbox{ where } H=\langle A, B\rangle.$ The problem that I have is ...
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### Matrix spectral decomposition

Let $A$ be a square matrix $(N \times N)$ and $a_{ij} \in \mathbb{R}$. Suppose A has N eigenvalues $\lambda_{1} < \lambda_{2} < ...\lambda_{n} \in \mathbb{R}$. $A$ = $R \Omega R^{-1}$ its ...
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If I have data $a,b,c,d$, and want to calculate $x=a+b-c-d$, $y=a-b-c+d$ and $z=a+b+c-d$, I can save three adds by doing $e=a-c$, $f=b-d$, then $x=e+f$,$y=e-f$, $z=a+c+f$. If I have 100 data values $... 0answers 235 views ### How to Diagonalize an Extremely Large Sparse Matrix in SLEPc/PETSc Dear Friends, Recently I have started with learning SLEPc/PETSc, but I didn't find a way to solve my problem. I have to solve a big sparse matrix which is a two dimensional quantum ... 0answers 150 views ### Existence criteria for the LU decomposition of a tridiagonal matrix In this link, the following result is presented without proof: Let$a, b, c$be the lower off diagonal, diagonal, and upper off diagonal elements of a tridiagonal matrix. A pivotless LU ... 0answers 475 views ### About the Generalized singular value decomposition (GSVD). I have studied about Singular value decomposition (SVD) and had solved few numerical examples to understand SVD. Now I am studying Generalized singular value decomposition (GSVD). I followed this ... 0answers 42 views ### Algorithm to compute similarity computation I have a similarity transformation of matrices from the type$B = P^{-1}AP$. It is known that$A$and$P$are invertible matrices, but not orthogonal. Given that I have the matrices$P$and$A$I ... 0answers 605 views ### Multigrid Interpolation and Restriction operators I have a question about the restriction and the interpolation operators of a Multigrid algorithm. Let those be given: The full weighting restriction stencil (in 2D):$\frac{1}{16} \left[ \begin{...
I apologize in advance if this is an ill-posed question -- I'd appreciate advice on what pieces are missing as much as an answer. I'm solving a system like $P \approx X Y^T$, where P is a large ...