Geodesic
Positive matrices and eigenvectors†
Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 27-30

Voir la notice de l'article provenant de la source Cambridge University Press

For i, j = 1, 2, ..., let aij be real. A matrix A = (aij) will be called positive (A>0) or non-negative (A≧0) according as, for all i and j, aij>0 or aij≧0 respectively. Correspondingly, a real vector x = (x1, x2, ...) will be called positive (x>0) or non-negative (x≧0) according as, for all i, xi>0 or x≧0. A matrix A is said to be bounded if ∥ Ax ∥ ≦M ∥ x ∥ holds for some constant M, 0 ≦ M < ∞, and all x in the Hilbert space H of real vectors x = (x1, x2, ...) satisfying . The least such constant M is denoted by ∥ A ∥. If x and y belong to H, then (x, y) will denote as usual the scalar product Σxiyi. Whether or not x is in H, or A is bounded, y = Ax will be considered as defined bywhenever each of the series of (1) is convergent. 
Putnam, C. R. Positive matrices and eigenvectors†. Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 27-30. doi: 10.1017/S2040618500034651
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