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comment An inequality about Hermitian matrices
In inequality 9 of Terence Tao's notes that I had linked to, does he need a special basis to define his diagonal elements or will any basis do?
Nov
25
comment An inequality about Hermitian matrices
It would be great if you can help sort this out - also there was this related question that you could also help with - math.stackexchange.com/questions/1033848/…
Nov
25
comment An inequality about Hermitian matrices
and do you understand what jflipp is saying in the comment? - isn't Terence Tao's link's equation 9 not valid in every basis? Do I need a special basis to define the diagonal entries for the inequality to hold?
Nov
25
comment An inequality about Hermitian matrices
Well - the proof to that polytope lemma in your wiki link is not obvious to me - if that lemma is understood then my original question gets automatically answered.
Nov
25
comment An inequality about Hermitian matrices
@dileep Isn't the assumption statement that I have written (which is equation 9) of the link above, a stronger statement than the majorization statement?
Nov
25
comment An inequality about Hermitian matrices
I am trying to understand how Terence Tao in his notes somehow thinks that polytope statement follows from this inequality I wrote - see around equation 9 in these notes.terrytao.wordpress.com/2010/01/12/…
Nov
25
comment An inequality about Hermitian matrices
@jflipp Isn't what you are saying contradicting the Schur-Horn theorem? I thought that is the whole point of that to say that this sceanrio you describe is not possible - the diagonal n-tuple is always in the convex hull of the permutations of the eigenvalue n-tuples.
Nov
24
asked An inequality about Hermitian matrices
Nov
24
comment What is the multiplicity of the largest eigenvalue of a graph?
@Exodd But that is the smallest eigenvalue of the Laplacian of the regular graph - right? You know anything about the largest Laplacian eigenvalue in general?
Nov
24
suggested suggested edit on An analytic characterization of eigenvalues of a Hermitan matrix.
Nov
24
asked What is the multiplicity of the largest eigenvalue of a graph?
Oct
2
comment Is there a relationship between the clique of a graph and colouring of a graph?
May be you can give the example you have in mind about triangle free graph with arbitrarily large chromatic number.
Sep
30
comment Is there a relationship between the clique of a graph and colouring of a graph?
Thanks! Can you kindly explain the intuition behind behind being triangle free?
Sep
30
asked Is there a relationship between the clique of a graph and colouring of a graph?
Sep
27
comment A question about similarity transformation.
I want to disallow anything that would obviously lead to isomorphic graphs. I believe such an orbit does exist inside the group of transformations which would most often not lead to isomorphic graphs but would keep producing an infinite family of such graphs. I would think of it as 2 possible separate question (1) find a curve c(t) : [0,1] -> O(n) such that c(t)Ac(t)^{-1} is almost always some non-isomorphic d-regular adjacency matrix OR (2) find a B in O(n) such that B^kA(B^-1)^k is almost always some non-isomorphic d-regular adjacency matrix. I don't know which way of thinking is easier!
Sep
27
comment A question about similarity transformation.
@ChrisGodsil Yes I am thinking of cospectral regular graphs! :D I guess I should have said that I want non-trivial similarity transformations!
Sep
27
asked A question about similarity transformation.
Sep
22
comment Solving (for asymptotics) of certain recurrence equations.
So did you just guess this out of thin air?
Sep
21
comment Solving (for asymptotics) of certain recurrence equations.
The question is how do you guess that correct answer? I am quite certain that if you tweaked the coefficient of even of of the "T"s on the right then this guess would not have worked. Is there is a method?
Sep
21
asked Solving (for asymptotics) of certain recurrence equations.