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- W2091214735 abstract "For i, j = 1, 2, …, let a ij be real. A matrix A = ( a ij ) will be called positive ( A >0) or non-negative ( A ≧0) according as, for all i and j , a ij >0 or a ij ≧0 respectively. Correspondingly, a real vector x = ( x 1 , x 2 , …) will be called positive ( x >0) or non-negative ( x ≧0) according as, for all i , x i >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 = ( x 1 , x 2 , …) 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 Σ x i y i . Whether or not x is in H , or A is bounded, y = Ax will be considered as defined by whenever each of the series of (1) is convergent." @default.
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- W2091214735 date "1963-01-01" @default.
- W2091214735 modified "2023-10-18" @default.
- W2091214735 title "Positive matrices and eigenvectors" @default.
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- W2091214735 doi "https://doi.org/10.1017/s2040618500034651" @default.
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