The exponent set of symmetric primitive (0, 1) matrices with zero trace
نویسندگان
چکیده
منابع مشابه
The kth upper generalized exponent set for the class of non-symmetric primitive matrices
Let QBn be the set of n x n (n > 8) non-symmetric primitive matrices with at least one pair of nonzero symmetric entries. For each positive integer 2 ::; k ::; n 2, we give the kth upper generalized exponent set for Q Bn by using a graph theoretical method.
متن کاملThe kth upper generalized exponent set for primitive matrices
Let Pn,d be the set of n x n non-symmetric primitive matrices with exactly d nonzero diagonal entries. For each positive integer 2 ~ k ~ n -1, we determine the kth upper generalized exponent set for Pn,d and characterize the extremal matrices by using a graph theoretical method.
متن کاملPrimitive Zero-Symmetric Sign Pattern Matrices with Zero Diagonal Attaining the Maximum Base
A sign pattern matrix or sign pattern A is a matrix whose entries are from the set {1,−1, 0}. Notice that for a square sign pattern matrixA, in the computation of the signs of the entries of the power A, an ambiguous sign may arise when a positive sign is added to a negative sign. So a new symbol # was introduced in 1 to denote such an ambiguous sign. The powers of a square sign pattern have be...
متن کاملPower Indices of Trace Zero Symmetric Boolean Matrices
The power index of a square Boolean matrix A is the least integer d such that A is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n × n primitive symmetric Boolean matrices of trace zero, the class of n × n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zer...
متن کاملOn Approximation Problems With Zero-Trace Matrices
12 because the conditions formulated in Corollary 1 are satissed for the problem (??). Therefore we have for every z 2 C jjjI + zBjjj k jjjIjjj k : Hence for every unitarily invariant norm we have by the properties of the unitarily invariant norms jjI + zBjj jjIjj: This completes the proof. 2 The above considerations imply that the characterization of a zero-trace matrix by means of the problem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90244-7