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Some counting questions for matrices with restricted entries

✍ Scribed by I.E. Shparlinski

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
123 KB
Volume
432
Category
Article
ISSN
0024-3795

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✦ Synopsis

We obtain upper bounds for the number of arbitrary and symmetric matrices with integer entries in a given box (in an arbitrary location) and a given determinant. We then apply these bounds to estimate the number of matrices in such boxes which have an integer eigenvalues. Finally, we outline some open questions.

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Some Properties of Matrices with 1, -1 a
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A class of matrices with 1, -1 and 0 entrim, called the H-matrices, i8 introduced and properties of such matrices are investigated. It k shown that for an H-matrix K the matrix B = KDKT, where D is a diagonal matrix with nonnegative diagonal entries, ha8 certain properties applicable to topological