Taiwanese Journal of Mathematics

On Inverse Eigenvalue Problems of Quadratic Palindromic Systems with Partially Prescribed Eigenstructure

Kang Zhao, Lizhi Cheng, Anping Liao, and Shengguo Li

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The palindromic inverse eigenvalue problem (PIEP) of constructing matrices $A$ and $Q$ of size $n \times n$ for the quadratic palindromic polynomial $P(\lambda) = \lambda^2 A^{\star} + \lambda Q + A$ so that $P(\lambda)$ has $p$ prescribed eigenpairs is considered. This paper provides two different methods to solve PIEP, and it is shown via construction that PIEP is always solvable for any $p$ ($1 \leq p \leq (3n+1)/2$) prescribed eigenpairs. The eigenstructure of the resulting $P(\lambda)$ is completely analyzed.

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Taiwanese J. Math., Advance publication (2019), 24 pages.

First available in Project Euclid: 4 March 2019

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Primary: 65F18: Inverse eigenvalue problems 65F15: Eigenvalues, eigenvectors 15A24: Matrix equations and identities 15A29: Inverse problems

quadratic palindromic system inverse eigenvalue problem partially prescribed eigendata


Zhao, Kang; Cheng, Lizhi; Liao, Anping; Li, Shengguo. On Inverse Eigenvalue Problems of Quadratic Palindromic Systems with Partially Prescribed Eigenstructure. Taiwanese J. Math., advance publication, 4 March 2019. doi:10.11650/tjm/190203. https://projecteuclid.org/euclid.twjm/1551690151

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