All Questions
Tagged with analytic-geometry linear-algebra
4
questions
12
votes
2
answers
576
views
The $r$-dimensional volume of the Minkowski sum of $n$ ($n\geq r$) line sets
Let $n$ line sets be $\mathcal{S}_i=\{a\mathbf{h}_i:0 \le a \le 1\}$, for $1 \le i \le n$, where $\{\mathbf{h}_1,\cdots,\mathbf{h}_n\}$ is a vector group of rank $r$ in the $r$-dimensional Euclidean ...
- 550
5
votes
0
answers
495
views
How to compute the volume of a region transformed by a matrix?
This is a rewrite of the OP's question to emphasize what I think are the research level issues here.
Let $\mathscr{R}$ be a bounded convex body in $\mathbb{R}^n$ and let $H : \mathbb{R}^n \to \mathbb{...
- 550
3
votes
0
answers
520
views
Understanding canonical angles between two subspaces
I am trying to understand Wedin Theorem on the perturbations of the Singular Vectors of a matrix, and a key element for this theorem is the matrix of the canonical angles between two subspaces; I am ...
0
votes
1
answer
250
views
Some questions related to the unitary operators
A unitary operator is a surjective linear operator between complex inner product spaces, which preserves the inner product.
What is the name of the analogue for the real case? Orthogonal operator ...
- 5,275