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Results tagged with linear-algebra
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user 799
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
4
votes
2
answers
322
views
Algebra with elements x, y such that r(x)=r(y) for all finite-dimensional modules r
I'm interested in finding an algebra with elements x,y which are identified by every finite-dimensional module. I'm primarily interested in the case that everything is over the complex field, but answ …
- 2,513
-2
votes
1
answer
468
views
Little conjecture about sums of reciprocals
Given a finite list $x_i$ of $N$ positive reals, it seems that $\sum_{i=1}^N x_i = \sum_{i=1}^N x_i {}^{-1} \Rightarrow \sum_{i=1}^N x_i \geq N$. Can anyone give me a proof?
- 2,513
2
votes
1
answer
184
views
Partial isometries making families of linearly independent vectors orthogonal
Suppose I have a family of $n$ linearly-independent elements $v_i$ of the Hilbert space $\mathbb{C}^m$, which are not necessarily orthogonal. Can I always find a partial isometry $f: \mathbb{C} ^m \to …
- 2,513