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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.