# Questions tagged [matrix]

For questions about using and representing matrices on a computer in order to solve computational problems. Should generally also include a tag about the specific property/problem you are solving (e.g. [tag:linear-algebra], [tag:eigenvalues], [tag:inverse].

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### Wanted: sequences of linear systems for recycling Krylov solver analysis

In the solution of sequences of linear systems $$A_ix_i=b_i\quad\text{for}\quad i=1,2,\dots$$ with Krylov subspace methods, data can be recycled from already solved linear systems in order to speed up ...
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### What is fastest method for finding the minimum and maximum eigenvalues of a (possibly very large) symmetric matrix?

What is the best way to find the extreme eigenvalues - in order to find the spectral radius - of a general real dense symmetric matrix? Looking at similar questions e.g.: What's the most efficient ...
60 views

### Is there any matlab built-in function or libraries to calculate $\frac{d(\ln A)}{dA}$?

we can first conduct spectral decomposition of an positive definite isotropic tensor $A$ and then we can define $\ln(A)$, then we can define the frechet derivative of it, but how to calculate this in ...
115 views

### Optimized Lanczos method for finding eigenvalues of $A \otimes B$

Recently my supervisor told me about an efficient way to calculate eigenvalues and eigenvectors of matrix $A \otimes B$ with $a_{1} \times a_{2}$ as dimensions of $A$ and $b_{1} \times b_{2}$ is of $B$...
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### Lumped (diagonal) vs. consistent (non-diagonal, symmetric) mass matrix in Nastran

I've been tinkering with DMAP to explore the procedure followed by Nastran when solving a complex modes analysis. I've reached a passage I cannot understand: at some point Nastran formulated what it ...
74 views

### What do diagonal (DOF-to-self) terms of stiffness matrix physically mean?

I am used to interpreting each entry of a solid mechanic system's stiffness matrix as a 1D (linear or angular) spring joining one DOF (column index) to another (row index). But this interpretation ...
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57 views

### Orthogonal Transformation of Hessenberg Matrices

$H\in\mathbb{R}^{n\times n}$ is an upper Hessenberg matrix. Suppose $\lambda$ is an eigenvalue of $H$ and $x$ is an eigenvector w.r.t. $\lambda$. Is there any fast algorithm that can find an ...
249 views

### Reordering eigenvalues in Schur factorization - MATLAB ordschur and LAPACK dtrsen not producing the same results

Disclaimer: I previously posted this on SO, but though it would be more relevant for scicomp. The original post has been deleted. I have been trying to recreate the functionality provided by MATLABs <...
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### Is there a permutation used in sparse QR factorizations that better locates small elements on the diagonal of R?

Is there a permutation used in sparse QR factorizations that better locates small elements on the diagonal of R to the end of the diagonal? As an example, consider the following snippet of MATLAB ...