Doubly Stochastic Matrix/birkhoff Polytope and Birkhoff-von Neumann Theorem

Famous quotes containing the words doubly, matrix, neumann and/or theorem:

    A man calumniated is doubly injured—first by him who utters the calumny, and then by him who believes it.
    Herodotus (c. 484–425 B.C.)

    As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.
    Margaret Atwood (b. 1939)

    It means there are times when a mere scientist has gone as far as he can. When he must pause and observe respectfully while something infinitely greater assumes control.
    —Kurt Neumann (1906–1958)

    To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
    Albert Camus (1913–1960)