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Results tagged with linear-algebra
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user 19899
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
0
answers
254
views
Solve $(A+B)x=y$ given Cholesky decomposition of A and B
I wish to solve for $x$ in
$$
(A+B)x=y
$$
given square symmetric matrices $A$ and $B$. For certain reasons I have already computed the Cholesky decompositions for A and B:
$$
A = L^T L
$$
$$
B = M^ …
- 561
1
vote
1
answer
96
views
Cholesky factorization of planar graphs
Suppose the sparsity pattern of $A \in \mathbb{R}^{N \times N}$ is a planar graph. Can I use this to bound the complexity of solving
$$
Ax = b
$$
?
In particular, I was hoping to use the planar sep …
- 561
12
votes
1
answer
5k
views
Closest 3D rotation matrix in the Frobenius norm sense
Given a 3 by 3 matrix $M$ I would like to find the rotation matrix $R$ minimizing the Frobenius norm:
\begin{equation}
\|R-M\|_F
\end{equation}
Is there a closed form solution for $R$, or is it po …
- 561