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5 votes

Fill-reducing ordering for computing the matrix product $A^T A$?

That is not possible. If $P$ and $Q$ are permutation matrices, then their inverses, respectively, are $P^T$ and $Q^T$. Also note that, applying permutations to a matrix $A$ doesn't change its number ...
Abdullah Ali Sivas's user avatar
4 votes

Weird runtime behavior of `scipy.linalg.solve_triangular` and `trtrs`

Thanks to Federico Poloni's comment, I have revised the script as below. It looks like scipy.linalg.solve_triangular has time complexity $O(p^2)$, because the ...
nalzok's user avatar
  • 181
1 vote

Efficient projection onto the kernel of a matrix

The complement of the null space, $Z^\perp$, is of course spanned by the rows of the matrices $A_i$. If $Nm$ is relatively small, you can compute an orthonormal basis of $Z^\perp$ by running the Gram-...
Wolfgang Bangerth's user avatar
0 votes

Efficient projection onto the kernel of a matrix

If $n$ is sufficiently small you can compute $M= \sum_i A_i^T A_i$ which is $n\times n$. The projection on its kernel can be written as $P_M = I - MM^{+}$. So say you have a vector $v$ and you want to ...
lightxbulb's user avatar
  • 1,994

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