منابع مشابه
Fully Indecomposable Exponents of Primitive Matrices
If A is a primitive matrix, then there is a smallest power of A (its fully indecomposable exponent) that is fully indecomposable, and a smallest power of A (its strict fully indecomposable exponent) starting from which all powers are fully indecomposable. We obtain bounds on these two exponents.
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Let n, r be integers with 0 ≤ r ≤ n− 1. An n×n matrix A is called r-partly decomposable if it contains a k×l zero submatrix with k+l = n−r+1. A matrix which is not r-partly decomposable is called r-indecomposable (shortly, r-inde). Let Eij be the n × n matrix with a 1 in the (i, j) position and 0’s elsewhere. If A is r-indecomposable and, for each aij 6= 0, the matrix ∗Research supported by Nat...
متن کاملOn Indecomposable Normal Matrices in Spaces with Indefinite Scalar Product
Finite dimensional linear spaces (both complex and real) with indefinite scalar product [·, ·] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in terms of specific functions of v = min{v − , v+}, where v− (v+) is the number of negative (positive) squares of the form [x, x]. All the bounds except for one...
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Let χ1(n) denote the maximum possible absolute value of an entry of the inverse of an n by n invertible matrix with 0, 1 entries. It is proved that χ1(n) = n 1 2. This solves a problem of Graham and Sloane. Let m(n) denote the maximum possible number m such that given a set of m coins out of a collection of coins of two unknown distinct weights, one can decide if all the coins have the same wei...
متن کاملOn Induced Projective Indecomposable Modules
A well-known theorem of Fong states that over large enough fields of any characteristic, the principal indecomposable modules of a soluble finite group are induced from subgroups of order prime to the characteristic. It is shown that this property in fact characterises soluble finite groups.
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1971
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(71)80018-1