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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
Jul
14
comment A metric for Grassmannians
"Natural" metrics on the Grassmannian should be invariant under isometries of the undelying Euclidian space. Actually there are many such metrics, and this nice paper gives a general method for constructing them: Qiu, Zhang, Li, "Unitarily invariant metrics on the grassmann space". SIAM J. Matrix. Anal. Appl. vol 27, no 2, 507-531.
Jul
10
comment Kalinin's formulation of the Anosov closing lemma
Guess you meant: The point $y$ is obtained by taking the intersection of the local stable set of $p$ with the nth pull-back of the local unstable set of $f^n(x)$.
May
5
revised Generalizations and relative applications of Fekete's subadditive lemma
Allow infinity values.
Apr
9
comment Rationality of translation lengths in hyperbolic groups
@lee-mosher Is it really true that "the expression d(1,g^n)/n achieves its limit at some finite value n=N independent of g"? In the free group of two generators a, b, if g=bab^{-1} then d(1,g^n)/n=(n+2)/n. Am I missing something stupid? Or is it necessary to replace g by an appropriate conjugate element?
Mar
24
comment Continuous maps which send intervals of $\mathbb{R}$ to convex subsets of $\mathbb{R}^2$
This is the Mihalik-Wieczorek problem. It's indeed devilish. :) Let me remark that if you only ask for the convexity of $f(I)$ for the intervals of the form $I=[0,t]$ then it is possible to construct a space-filling curve: see arxiv.org/abs/1407.5204 and the references there.
Mar
19
awarded  Explainer
Mar
18
answered A metric for Grassmannians
Mar
18
awarded  Excavator
Mar
18
awarded  Organizer
Mar
18
revised A metric for Grassmannians
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