Jairo Bochi
Reputation
545
Next privilege 1,000 Rep.
 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