We define as minimally strategy-proof a rank aggregation rule that cannot be manipulated with respect to at least one order extension. We characterize the class of minimal strategy-proof rules. Based on this characterization, we show that most rules considered in Bossert and Sprumont ( 2014 ) ...
Answer to: Prove that rank(A) = rank(AA'). By signing up, you'll get thousands of step-by-step solutions to your homework questions. You can also...
(2.1) and its generalization to n variables, a square matrix is assigned a rank equal to the number of linearly independent forms that its elements describe. Thus, a nonsingular n× n matrix will have rank n, while a n× n singular matrix will have a rank r less than n. The rank ...
Let (G, H) be one of the equal rank reductive dual pairs $$\left( Mp_{2n},O_{2n+1} \right) $$ or $$\left( U_n,U_n \right) $$ over a nonarchimedean
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By a similar approach, we can also show a rank formula for the linear combination a1P+a2Q of a pair of idempotent matrices P and Q. Theorem 2.2 Let P and Q be a pair of idempotent matrices of order m, and let a1 and a2 be two nonzero scalars such that a1+a2≠0. Then(2.10)r...
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puce T'(Ni) is extremul for k,( T, Ma, Nk). The proof involves only straightforward calculations. The final result of this section is a duality theorem. 46 A. L. BROWN 1.2.2. THEOREM. IfdimE~n+b,dimF~n+bandTE~(E,F)isa compact linear operator then Proof: This result in the ...