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• ... Let A be doubly stochastic. Birkhoff s Theorem says that there are positive numbers a1,...,an and permutation matrices, P1,...,Pn such that a1 + ... + an =
Message 1 of 5 , Mar 31, 2002
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--- In mathforfun@y..., vbist61 <no_reply@y...> wrote:
> The operator norm of a doubly stochastic matrix is at most 1. Prove

Let A be doubly stochastic. Birkhoff's Theorem says that there are
positive numbers a1,...,an and permutation matrices, P1,...,Pn such
that a1 + ... + an = 1 and A = a1P1 + ... + anPn. Since |P| = 1 for
all permutation matrices, the claim follows by applying the triangle
inequality.
• The operator norm of a doubly stochastic matrix. Sound like a medicla condition. Nurse, I think I m hemorrhaging from the operator norm of the doubly
Message 1 of 5 , Apr 2, 2002
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The operator norm of a doubly stochastic matrix. Sound like a
medicla condition.

"Nurse, I think I'm hemorrhaging from the operator norm of the doubly
stochastic matrix!! Get me a doctor!!!"

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