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Results tagged with linear-algebra
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user 805482
For questions on linear algebra, including vector spaces, linear transformations, systems of linear equations, spanning sets, bases, dimensions and vector subspaces.
2
votes
Inequality after multiplying inverse
I just found an counterexample:
Let $A = \pmatrix{2 & -1 \\ -1 & 1}$, $x = \pmatrix{-1 \\ 0}$ and $b = \pmatrix{0 \\ 0}$.
$A$ is positive definite, as both eigenvalues are positive.
$A\cdot x = \pma …
- 779
1
vote
1
answer
33
views
Inequality after multiplying inverse
Let $A$ be a positive definite, symetrical matrix.
Is it true, that
$A\cdot x \leq b$ $\Leftrightarrow$ $x \leq A^{-1}\cdot b$.
It is clear, that if $A$ is positive definite, than $A$ must be invertib …
- 779
1
vote
1
answer
34
views
Inequality of norm in two cases [closed]
I am currently trying to understand why the following inequality holds for $d_2>d_1>0$ and $\eta >0$, $x= (0,t)$ or $x=(t,t)$ for $t\geq 0$
$||d-\eta x|| \geq \text{min}\{|d_1|, \frac{\sqrt{2}}{2}|d_2 …
- 779
2
votes
1
answer
63
views
Group algebra for finitely generated group
I know the definition of a group algebra $k[G]$ for a finite group $G$ as the set of all linear combination of elements in $G$ with coefficients in the field $k$.
Here, it is easy to show that this is …
- 779