Equalities and Inequalities for Norms of Block Imaginary Circulant Operator Matrices

Circulant, block circulant-type matrices and operator norms have become effective tools in solving networked systems. In this paper, the block imaginary circulant operator matrices are discussed. By utilizing the special structure of such matrices, several norm equalities and inequalities are presented. The norm τ in consideration is the weakly unitarily invariant norm, which satisfies τA=τ(UAV). The usual operator norm and Schatten p-norm are included. Furthermore, some special cases and examples are given

Algorithms for Finding Inverse of Two Patterned Matrices over Z

Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over Zp which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given