Functions preserving rank-$k$ matrices of order $n$ over fields
نویسندگان
چکیده
منابع مشابه
NUMBER OF RANK r SYMMETRIC MATRICES OVER FINITE FIELDS
We determine the number of n×n symmetric matrices over GF (p) that have rank r for 0 ≤ r ≤ n. In [BM2] Brent and McKay determine the number of n × n symmetric matrices over Zp that have determinant zero. Thus they determine the number of n× n symmetric matrices over Zp that have rank n. We extend their result to symmetric matrices over GF (p) and we determine the number of matrices that have ra...
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Let M be a random matrix over GFq] such that for each entry M ij in M and for each non-zero eld element the probability PrrM ij = ] is p=(q ? 1), where p = (log n ? c)=n and c is an arbitrary but xed positive constant. The probability for a matrix entry to be zero is 1?p. It is shown that the expected rank of M is n ? O(1): Furthermore, there is a constant A such that the probability that the r...
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In this thesis we are concerned with themes suggested by rank properties of subspaces of matrices. Historically, most work on these topics has been devoted to matrices over such fields as the real or complex numbers, where geometric or analytic methods may be applied. Such techniques are not obviously applicable to finite fields, and there were very few general theorems relating to rank problem...
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Abstract. Define the weight of a matrix to be the number of non-zero entries. One would like to count m by n matrices over a finite field by their weight and rank. This is equivalent to determining the probability distribution of the weight while conditioning on the rank. The complete answer to this question is far from finished. As a step in that direction this paper finds a closed form for th...
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We want to achieve efficient exact computations, such as the rank, of sparse matrices over finite fields. We therefore compare the practical behaviors, on a wide range of sparse matrices of the deterministic Gaussian elimination technique, using reordering heuristics, with the probabilistic, blackbox, Wiedemann algorithm. Indeed, we prove here that the latter is the fastest iterative variant of...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2005
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2005.100