Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599524 | Linear Algebra and its Applications | 2014 | 20 Pages |
Abstract
The inverse eigenvalue problem for T-alternating matrix polynomials over arbitrary algebraically closed fields of characteristic different from two is considered. The main result shows that the necessary conditions obtained in [9] for a matrix polynomial to be the Smith form of a T-alternating matrix polynomial are under mild conditions also sufficient to be the Smith form of a T-alternating matrix polynomial with invertible leading coefficient which is additionally in anti-triangular form. In particular, this result implies that any T-alternating matrix polynomial with invertible leading coefficient is equivalent to a T-alternating matrix polynomial in anti-triangular form that has the same finite and infinite elementary divisors as the original matrix polynomial. Finally, the inverse eigenvalue problem for T-palindromic matrix polynomials is considered excluding the case that both +1 and â1 are eigenvalues.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Leonhard Batzke, Christian Mehl,