Abstract
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.
Citation
Kang Zhao. Lizhi Cheng. Anping Liao. Shengguo Li. "On Inverse Eigenvalue Problems of Quadratic Palindromic Systems with Partially Prescribed Eigenstructure." Taiwanese J. Math. 23 (6) 1511 - 1534, December, 2019. https://doi.org/10.11650/tjm/190203
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