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Results tagged with linear-algebra
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user 6153
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
trace of a matrix of finite order
You have a (real) linear representation r of the cyclic group C of order d; you give its character, and then ask for the character of a certain subrepresentation of the tensor product of r and its dua …
- 12.6k
1
vote
How do you compute the dual norm of an induced norm on a subspace of a finite-dimensional $\...
This is a fairly general case of the Legendre transformation, I guess. I don't really see that it should be that much simpler than the general case (but I'm not an expert).
- 12.6k
3
votes
Is Diagonalization worth to be taught?
You are talking about training in mathematics, not numerical analysis, so the answer is surely "yes". What is more, given that software packages exist, it should be taught in a more conceptual way tha …
3
votes
Determining a recurrence relation
I'd certainly expect to acquire some useful information by modular arithmetic, in a given situation. For example modulo a prime p, if there is a linear recurrence, then the sequence of residues must a …
- 12.6k
1
vote
Parametrization of O(3)
If there were a really simple way we wouldn't need the concept of "gimbal lock" (http://en.wikipedia.org/wiki/Gimbal_lock). In other words the manifold in question is compact but isn't the 3-torus, an …
- 12.6k
2
votes
Accepted
Morphisms between representations
Isn't this just a fancy way of talking about the cycle decomposition of a permutation? The language you use is a little imprecise. But, firstly, by change of basis P can be made into a block matrix fo …
- 12.6k
2
votes
Is there a field which is the union of finitely many proper subfields?
The reason it fails in the case of finite fields is the primitive element theorem (over the prime subfield, even). This is not quite an argument in the general case because of possible inseparability. …
- 12.6k
12
votes
Accepted
To what extent can algorithms in undergraduate linear algebra be made continuous/polynomial/...
There are perhaps three or four themes lurking in here. NB that "undergraduate linear algebra" is perhaps an artificial construct, and examples set to test whether students understand basic concepts d …
- 12.6k
-1
votes
Splitting the determinant polynomial into linear factors - a Dedekind problem
I don't know why you say the Dedekind problem is "forgotten": the Dedekind determinant is discussed in number theory books. The factorisation for the regular representation for general finite groups w …
- 12.6k
3
votes