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Results tagged with linear-algebra
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user 158036
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
1
answer
107
views
Bounds on $\operatorname{sgn}(Au) - \operatorname{sgn}(Av)$ when $\|u-v\|_1 \leq \epsilon$
$\DeclareMathOperator\sgn{sgn}$Suppose A is a $N \times N$ Hermitian and unitary matrix, i.e., $A^{\dagger}=A$ and $A^{\dagger}A=I =AA^{\dagger}$. (Assume all entries are real.)
And let $u \in \{-1,1 …
- 221
7
votes
Bounds on $\operatorname{sgn}(Au) - \operatorname{sgn}(Av)$ when $\|u-v\|_1 \leq \epsilon$
There is a straightforward bound.
Consider A to be the $\log(N)$-fold tensor product of $H= \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$.
A is Unitary and Hermitian. In fact A …
- 356