A trace bound for integer-diagonal positive semidefinite matrices
نویسندگان
چکیده
منابع مشابه
A Trace Bound for Positive Definite Connected Integer Symmetric Matrices
Let A be a connected integer symmetric matrix, i.e., A = (aij) ∈ Mn(Z) for some n, A = AT , and the underlying graph (vertices corresponding to rows, with vertex i joined to vertex j if aij 6= 0) is connected. We show that if all the eigenvalues of A are strictly positive, then tr(A) ≥ 2n− 1. There are two striking corollaries. First, the analogue of the Schur-SiegelSmyth trace problem is solve...
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ژورنال
عنوان ژورنال: Special Matrices
سال: 2020
ISSN: 2300-7451
DOI: 10.1515/spma-2020-0002