LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM

This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented

A Hub Matrix Theory and Applications to Wireless Communications

This paper considers communications and network systems whose properties are characterized by the gaps of the leading eigenvalues of for a matrix . It is shown that a sufficient and necessary condition for a large eigen-gap is that is a "hub" matrix in the sense that it has dominant columns. Some applications of this hub theory in multiple-input and multiple-output (MIMO) wireless systems are presented.</p

doi:10.1155/2007/13659 Research Article A Hub Matrix Theory and Applications to Wireless Communications

This paper considers communications and network systems whose properties are characterized by the gaps of the leading eigenvalues of A H A for a matrix A. It is shown that a sufficient and necessary condition for a large eigen-gap is that A is a “hub ” matrix in the sense that it has dominant columns. Some applications of this hub theory in multiple-input and multiple-output (MIMO) wireless systems are presented. Copyright © 2007 H. T. Kung and B. W. Suter. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1