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Results tagged with linear-algebra
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user 97148
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
10
votes
The rank of a perturbed triangular matrix
For $n=10$ there exists such a matrix of rank(4) (see below).
Hence we can improve the upper bound to $c=\log_{10}(4)=0.6021$. I found this matrix using matlab. However I did not find any solution wi …
- 198
1
vote
Accepted
tighter bound on the sum of sub-matrices
$$\left\|\sum A_iv_i\right\|=\sup_{\|x\|=1} \left\|\sum A_iv_ix\right\|\leq \sup_{\|x_i\|=|v_i|} \left\|\sum A_ix_i\right\|=\sup_{\|x_i\|=|v_i|} \left\|A \begin{pmatrix} x_1\\ \vdots\end{pmatrix}\righ …
- 198