On common invariant cones for families of matrices
Leiba Rodman, Hakan Seyalioglu, Ilya M. Spitkovsky
TL;DR
This paper investigates the existence and construction of common invariant cones for various families of real matrices, providing complete results for 2x2 matrices and diagonally similar matrices of any size, with special cases for matrices sharing a dominant eigenvector.
Contribution
It offers new comprehensive results on invariant cones for specific classes of matrices, including 2x2 and simultaneously diagonalizable matrices, extending previous understanding.
Findings
Complete characterization for 2x2 matrices
Results for families of simultaneously diagonalizable matrices
Analysis of matrices sharing a dominant eigenvector
Abstract
The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable matrices of any size. Families of matrices with a shared dominant eigenvector are considered under some additional conditions.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · graph theory and CDMA systems