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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. |