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May
2
comment Parametrization of O(3)
BTW, an interesting (though not very well written) Wikipedia article on the quaternion parametrization is this one: en.wikipedia.org/wiki/Euler%E2%80%93Rodrigues_formula
May
2
comment Parametrization of O(3)
Though this appeared in Neil Strickland's answer below, I mention for emphasis that the most useful answer is the quaternion parametrization of SO(3), a.k.a. Euler-Rodrigues formula: en.wikipedia.org/wiki/Euler%E2%80%93Rodrigues_formula
Apr
9
awarded  Necromancer
Mar
16
comment Applications of the Cayley-Hamilton theorem
@DenisSerre I don't believe in a total order on the set of proofs. BTW, the inequality in my proof can be extended to sets of matrices and, among other applications, used to prove a version of the Gelfand formula in this setting, namely, the Berger-Wang theorem.
Mar
15
awarded  Nice Answer
Mar
6
comment How do Schubert classes form a basis for $H^{*}(Gr(k, n))$?
When I studied this subject, I found this text very useful: www-personal.umich.edu/~jblasiak/grassmannian.pdf
Mar
3
revised Sets of matrices which are irreducible but not strongly irreducible
Improved explanation
Mar
1
answered Sets of matrices which are irreducible but not strongly irreducible
Mar
1
comment Sets of matrices which are irreducible but not strongly irreducible
Nice question! The second question should be reformulated to avoid the following trivial counterexample: Take a (sufficiently interesting) finite group of matrices and multiply all of them by 2016. Then the generated semigroup in not finite anymore.
Mar
1
answered Applications of the Cayley-Hamilton theorem
Feb
11
revised Spectra of certain totally positive matrices
added 1 character in body
Feb
11
revised Spectra of certain totally positive matrices
added 9 characters in body
Feb
11
revised Spectra of certain totally positive matrices
added 8 characters in body
Feb
11
revised Spectra of certain totally positive matrices
added reference for a weaker problem
Feb
11
asked Spectra of certain totally positive matrices
Jan
15
comment An inequality for the spectral radius of matrices used by J. Bochi
Oops! Actually the constant from Ian's proof depends on the norm of the identity matrix (which may be different from 1: for example for the Hilbert-Schmidt norm), and so I don't know if there is a uniform constant that works for all submultiplicative norms. Anyway, my comment makes sense if "submultiplicative norm" is replaced with "matrix norm induced by a norm in R^d".
Jan
15
comment An inequality for the spectral radius of matrices used by J. Bochi
Actually, as the proof shows, the inequality holds (with the same constant 2^d-1) for any submultiplicative norm on dxd matrices, and not just the Euclidian-induced one. So, in principle, the optimal constant may have different values, depending on whether we care only about the Euclidian-induced norm, or whether we want an inequality valid simultaneously for all submultiplicative norms.
Jan
5
comment Advice for PhD Supervisors
See this text by Anatole Katok: personal.psu.edu/axk29/reflections.html
Dec
5
comment What are the applications of immanants?
According to this paper dx.doi.org/10.1016/j.laa.2015.10.034, the conjecture is false.
Sep
29
awarded  Necromancer