## Abstract

Let A_{m} be a positive definite, m x m, Toeplitz matrix. Let A_{k} be its k x k principal minor (for any k≤m), which is also positive definite and Toeplitz. Define the central mass sequence {ρ{variant}_{1},...,ρ{variant}_{m}} by ρ{variant}_{k} = sup{ρ{variant}: A_{k} - ρ{variant}Π_{k} > 0}, in which Π_{k} is the k x k matrix of all 1's. We show how knowledge of the sequence {ρ{variant}_{k}} is equivalent to knowledge of the matrix A_{m}. This result has application to the direct and inverse problems for a transmission line which consists of piecewise constant components. Knowing the impulse response of the transmission line, we can calculate the capacitance taper of the line, and vice versa.

Original language | English (US) |
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Pages (from-to) | 207-225 |

Number of pages | 19 |

Journal | Linear Algebra and Its Applications |

Volume | 38 |

Issue number | C |

DOIs | |

State | Published - Jun 1981 |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics