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Results tagged with inner-product
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user 46290
6
votes
1
answer
280
views
Which metrics on exterior power are induced from metrics on the base?
$\newcommand{\id}{\text{id}}$
$\newcommand{\Hom}{\text{Hom}}$
This is a cross-post.
Let $V$ be a $d$-dimensional real vector space, and let $2 \le k \le d-1$. Every inner product on $V$ induces an inn …
- 6,741
2
votes
1
answer
230
views
Invariant characterization of isometric embeddings
$\newcommand{\Cof}{\operatorname{Cof}}$
$\newcommand{\Det}{\operatorname{Det}}$
$\newcommand{\Lam}{\operatorname{\Lambda}}$
Motivation (and the "classic" case):
I am trying to find a coordinate-free …
- 6,741
4
votes
1
answer
382
views
Existence of $SO(n)$-isotropic inner products which are not $O(n)$-isotropic
$\newcommand{\al}{\alpha}$
Let $M_n$ be the space of $n \times n$ real matrices.
Question:
For which $n$, is there an inner product on $M_n$ which satisfies:
$$(*) \, \, \langle Q^TXQ,Q^TYQ \rangl …
- 6,741