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Results tagged with norms
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user 102946
9
votes
1
answer
509
views
Regular $p$-norm of a matrix
Let $n \in \mathbb{N}$ and $p \in [1,\infty]$ be fixed and endow $\mathbb{C}^n$ with the $p$-norm $\|\cdot\|_p$. For every matrix $A \in \mathbb{C}^{n \times n}$ we denote the operator norm of $A$ as …
- 12.5k
26
votes
Accepted
What are the matrices preserving the $\ell^1$-norm?
As pointed out by YCor in the comments, the following theorem is true:
Theorem 1 Let $p \in [1,\infty] \setminus \{2\}$. If a matrix $A \in \mathbb{R}^{n \times n}$ is an isometry on $\mathbb{R}^n$ w …
- 12.5k