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On orderings induced by the Loewner partial ordering

100%

Hauke J. , Markiewicz A.

Applicationes Mathematicae

1993-1995

tom 22

nr 2

145-154

The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.

Stability of an Interval Matrix Symmetrizable by Distinct Diagonal Matrices

100%

Kowynia J.

2001

tom vol. 49, nr 3

433-443

Stability of convex combination of matrices symmetrizable by diagonal matrices is considered. Necessary and sufficient condition for stability of some interval matrix, symmetrizable by distinct diagonal matrices is proposed.