An improvement on Plessner's theorem
โ Scribed by Frederick Bagemihl
- Publisher
- Springer-Verlag
- Year
- 1969
- Tongue
- French
- Weight
- 183 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0025-5874
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let A E M,,. In terms of Perron roots and Perron vectors of two positive (or irreducible nonnegative) matrices that dominate principal submatrices A [ 1. . k] and A [k + 1, , n], respectively, we present an improvement on Ky Fan-s theorem of matrix eigenvalues.
Improving Bruck's Completion-Theorem for nets, we show that a net of order k and degree k + 1 -t5 can be extended to an affine plane, if 3k > 8t53 -18t52 + 8~5 + 4. As applications we obtain the following two theorems: A maximal partial t-spread in PG(2t + 1, q), q not a square, with deficiency ~ >
An n x n nonnegative matrix A is called primitive if for some positive integer k, every entry in the matrix Ak is positive or, in notation, A' + 0. The exponent of primitivity of A is defined to be y(A) = minjk E H, : Ah % 0}, where Z, denotes the set of positive integers. The well known Dulmage-Men