Some matrix inequalities in multiport network connections. (English) Zbl 0671.47018
The Gohberg anniversary collection, Vol. I: Matrix theory papers, Proc. Int. Conf. Oper. Theory., Calgary/Canada 1988, Oper. Theory, Adv. Appl. 40, 111-131 (1989).
Summary: [For the entire collection see Zbl 0669.00005.]
Connections of resistive multiport electrical networks give rise to several questions concerning comparisons among certain functions of impedance matrices of branch networks. In the present paper, some matrix inequalities, related to symmetric function means of an n-tuple of positive definite matrices, are proved to answer a part of the conjectures of W. N. Anderson jun., T. D. Morley and G. E. Trapp [Linear Algebra Appl. 60, 129-143 (1984; Zbl 0575.47001)].
Connections of resistive multiport electrical networks give rise to several questions concerning comparisons among certain functions of impedance matrices of branch networks. In the present paper, some matrix inequalities, related to symmetric function means of an n-tuple of positive definite matrices, are proved to answer a part of the conjectures of W. N. Anderson jun., T. D. Morley and G. E. Trapp [Linear Algebra Appl. 60, 129-143 (1984; Zbl 0575.47001)].
MSC:
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 47A60 | Functional calculus for linear operators |
| 94C15 | Applications of graph theory to circuits and networks |
