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Results tagged with linear-algebra
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user 479798
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
10
votes
2
answers
894
views
What norms can be "universally" defined on any real vector space with a fixed basis?
Let $V$ be a real vector space and let $B = (b_\lambda)_{\lambda \in \Lambda}$ be a basis. So every $v \in V$ can be written uniquely as a linear combination
$$ v = c_{\lambda_1} b_{\lambda_1} + c_{\l …
- 641
5
votes
1
answer
181
views
What is the "natural" or "physical" norm on the Hessian matrix (and other higher derivatives)?
Let $u : \mathbb R^n \rightarrow \mathbb R$ and let $H : \mathbb R^n \rightarrow \mathbb R^{n \times n}$ be its Hessian matrix. What is the "natural" choice of pointwise norm on the Hessian matrix?
He …
- 641