191 reputation
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bio website
location Washington University in St Louis
age 28
visits member for 3 years, 10 months
seen May 1 '13 at 4:44

Jul
2
awarded  Curious
Feb
2
comment system of homogeneous matrix equations
I do not know the background of this equation, the person who asked me this problem is working in algebraic geometry which I know nothing about. You answer is very helpful, are these the only solutions?
Feb
2
comment system of homogeneous matrix equations
I see, as a corollary of your conclusion, there is no solution if $n$ is not dividing the size of matrices, and $xA+yB$ will have distinct eigenvalues if $n$ equal to the size of matrices, are I right?
Feb
1
awarded  Commentator
Feb
1
comment system of homogeneous matrix equations
Sorry for not making the question clear, I am looking for matrices $A,B$ such that the identity holds for all $x,y$. I guess my terminology is incorrect.
Feb
1
revised system of homogeneous matrix equations
added 157 characters in body
Feb
1
awarded  Nice Question
Feb
1
asked system of homogeneous matrix equations
Jan
31
comment Interesting examples of minimal action on torus
@ Alain Valette @ Michele Triestino Thanks!
Jan
31
revised Interesting examples of minimal action on torus
added 104 characters in body
Jan
31
comment Interesting examples of minimal action on torus
@Lee Mosher Yes you are right, thanks for pointing this out. The correct statement should be that the functions $f_i$ are in suitable homotopy classes other than the one containing constant functions. The details are in Theorem 2.1 of Furstenberg's paper STRICT ERGODICTICY AND TRANSFORMATION OF THE TORUS and the remark after it.
Jan
29
revised Interesting examples of minimal action on torus
added 511 characters in body
Jan
29
revised Interesting examples of minimal action on torus
added 104 characters in body; added 20 characters in body; added 12 characters in body
Jan
29
asked Interesting examples of minimal action on torus
Jan
2
accepted Finite projection in Von Neumann algebra
Sep
28
asked Finite projection in Von Neumann algebra
Oct
8
awarded  Yearling
May
21
accepted Integral interpolation by polynomial
Apr
28
asked Integral interpolation by polynomial
Apr
1
comment About Turan`s problem(inequality) in multivariable
Since F(n) is homogeneous degree 0, F(n) always has a minimum point. If we take the gradient and set it to 0, we get a system of homogeneous polynomial equations(k equations and k variables), it seems that we should be able to solve it and thereafter find the minimum of F(n), but I've no idea of how to deal with such a system.