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Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite 1 The Birkhoff von Neumann Theorem states that any $ntimes n$ doubly stochastic matrix is a convex sum of permutation matrices. Is this true for $mathbbN times mathbbN$ matrices as well? (if yes, then can you give a reference?) linear-algebra discrete-mathematics game-theory share | cite | improve this question asked Jul 31 at 9:54 Yoav Rodeh 11 1 add a comment  |  up vote 1 down vote favorite 1 The Birkhoff von Neumann Theorem states that any $ntimes n$ doubly stochastic matrix is a convex sum of permutation matrices. Is this true for $mathbbN times mathbbN$ matrices as well? (if yes, then can you give a reference?) linear-algebra discrete-mathematics game-theory share | cite | improve this question asked Jul 31 at 9:54 Yoav Rodeh 11 1 add a comment  |  up vote 1 down vote favorite ...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite Let $G$ be a finite group and $H$ is a subgroup of $G$ where $[G:H]$ is $N$. Prove that there exists a subset $A$ of $G$ containing $N$ elements such that, $xH= yH $ implies $x=y$ and $Hx= Hy$ implies $x=y$ for all $x,y$ in $A$. This a problem from Basic Algebra by Jacobson. I dont have an idea how to start. Kindly provide hints. group-theory finite-groups share | cite | improve this question edited Jul 31 at 10:48 Alan Wang 4,088 9 30 asked Jul 31 at 10:04 tony 128 9 closed as off-topic by Derek Holt, John Ma, Mostafa Ayaz, amWhy, Isaac Browne Aug 1 at 0:47 This question appears to be off-topic. The users who voted to close gave this specific reason: " This question is missing context or other details : Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This in...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite 1 Knowing the eigenvalues of $A$, what we can say about the eigenvalues of $A+A^-1$? Is it true that $lambda_i,(A+A^-1) = lambda_i,A + frac1lambda_i,A$, where $lambda_i,A$ is the $i$-th eigenvalue of $A$? I ask this question after asking this question, due to the different opinion in the conversation in the comment. linear-algebra matrices eigenvalues-eigenvectors inverse share | cite | improve this question edited Jul 31 at 10:12 asked Jul 31 at 10:10 Alex 172 9 Consider $A$ already in Jordan normal form. Without loss, consider it is reduced to one block. What can be said about $A+A^-1$ in this situation? (Please always show the own work!) – dan_fulea Jul 31 at 10:13 Yes sorry, i just asked this question due to the comments in the conversation in a my previous question! – Alex Jul 31 at 10:16 ...