On approximation problems with zero-trace matrices

On 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...

Power 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...

Approximation Problems in the Riemannian Metric on Positive Definite Matrices

There has been considerable work on matrix approximation problems in the space of matrices with Euclidean and unitarily invariant norms. We initiate the study of approximation problems in the space P of all n×n positive definite matrices with the Riemannian metric δ2. Our main theorem reduces the approximation problem in P to an approximation problem in the space of Hermitian matrices and then ...

Cryptography on Trace-Zero Varieties

A Note on Eigenvalues Location for Trace Zero Doubly Stochastic Matrices