# Tagged Questions

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### Space of Distribution wrt to topology of uniformly convergence on bounded sets not Frechet-Space.

I found a state, that the Space of Distribution on (here:) $\mathbb{R}^{n}$, which is equipped with the topology of uniformly convergence on bounded subsets is not a Frechet Space. As far as i can ...
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### Does this question make any sense - eigenvalues and norms

Im having difficulties understanding this question: show that if $b$ is an eigenvector of an invertible matrix $A$ with an eigenvalue $\lambda_1$ and $\delta b$ is an eigenvector of $A$ with an ...
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### Prove triangle inequality of vector norm

I am trying to show that $||x+y||_p \leq ||x||_p + ||y||_p$ where $p$ is an integer larger than 1, but not infinity (I proved those cases already), and $||x||_p = (\sum_{i=1}^n |x_i|^p)^{\frac{1}{p}}$ ...
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### Consistency of matrix norm: $||Ax||_2 \leq ||A||_{Frobenius}||x||_2$

I'm trying to show that $||Ax||_2 \leq ||A||_{F}||x||_2$ where $A$ is an n by n matrix, $x\in \mathbb R^n$, $||x||_2$ is the euclidean norm, and $||A||_F$ is the frobenius norm. I actually wrote ...
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### Inequality with matrix norms

Prove that if $A$ is invertible and $||A-B||<||A^{-1}||^{-1}$ then $$\lVert (I-A)^{-1}\rVert \leq \frac{\lVert I\rVert-(\lVert I\rVert-1)\lVert A\rVert}{1-\lVert A\rVert}.$$ This is the second ...
Prove that if $A$ is invertible and $||A-B||<||A^{-1}||^{-1}$ then $$\lVert A^{-1} - B^{-1}\rVert \leq \lVert A^{-1}\rVert \frac{\lVert I-A^{-1}B\rVert}{1-\lVert I-A^{-1}B\rVert}.$$ I also need ...