A Note on J-positive Block Operator Matrices

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

A note on simultaneous block diagonally stable matrices

Ela a Note on Simultaneous Block Diagonally Stable Matrices

Abstract. Consider a set of square real matrices of the same size A = {A1, A2, . . . , AN}, where each matrix is partitioned, in the same way, into blocks such that the diagonal ones are square matrices. Under the assumption that the diagonal blocks in the same position have a common Lyapunov solution, sufficient conditions for the existence of a common Lyapunov solution with block diagonal str...

A note on “ 5 × 5 Completely positive matrices ”

In their paper “5×5 Completely positive matrices,” Berman and Xu [BX04] attempt to characterize which 5× 5 doubly nonnegative matrices are also completely positive. Most of the analysis in [BX04] concerns a doubly nonnegative matrix A that has at least one off-diagonal zero component. To handle the case where A is componentwise strictly positive, Berman and Xu utilize an “edge-deletion” transfo...