## Abstract

In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors {x_{i}} _{i=1}^{m} in C^{n} and a set of complex numbers {λ_{i}}_{i=1}^{m}, find a centrosymmetric or centroskew matrix C in R^{n×n} such that {x_{i}} _{i=1}^{m} and {λ_{i}}_{i=1}^{m} are the eigenvectors and eigenvalues of C, respectively. We then consider the best approximation problem for the IEPs that are solvable. More precisely, given an arbitrary matrix B in R^{n×n}, we find the matrix C which is the solution to the IEP and is closest to B in the Frobenius norm. We show that the best approximation is unique and derive an expression for it.

Original language | English |
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Pages (from-to) | 309-318 |

Number of pages | 10 |

Journal | Theoretical Computer Science |

Volume | 315 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 6 May 2004 |

Externally published | Yes |

## Keywords

- Centroskew matrix
- Centrosymmetric matrix
- Eigenproblem