𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Explicit construction of hyperdominant symmetric matrices with assigned spectrum

✍ Scribed by Dragan B. Kandić; Beresford Parlett; Branimir D. Reljin; Petar M. Vasić

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
346 KB
Volume
258
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

We prove by explicit construction the existence of at least one nontrivial symmetric hyperdominant matrix with assigned nonnegative spectrum. In addition, we construct symmetric matrices with assigned spectra and several specific nonhyperdominant types of sign patterns.

📜 SIMILAR VOLUMES

Existence and construction of nonnegativ
Existence and construction of nonnegative matrices with complex spectrum
✍ Oscar Rojo; Ricardo L. Soto 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 150 KB

The following inverse spectrum problem for nonnegative matrices is considered: given a set of complex numbers σ = {λ 1 , λ 2 , . . . , λ n }, find necessary and sufficient conditions for the existence of an n × n nonnegative matrix A with spectrum σ . Our work is motivated by a relevant theoretical

Existence and construction of nonnegativ
Existence and construction of nonnegative matrices with prescribed spectrum
✍ Ricardo L. Soto 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 139 KB

We consider the following inverse spectrum problem for nonnegative matrices: given a set of real numbers σ = {λ 1 , λ 2 , . . . , λ n }, find necessary and sufficient conditions for the existence of an n × n nonnegative matrix A with spectrum σ . In particular, by the use of a relevant theorem of Br

Fast construction of a symmetric nonnega
Fast construction of a symmetric nonnegative matrix with a prescribed spectrum
✍ O. Rojo; R. Soto; H. Rojo 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 578 KB

## In this paper, for a prescribed real spectrum, using properties of the circulant matrices and of the symmetric persymmetric matrices, we derive a fast and stable algorithm to construct a symmetric nonnegative matrix which realizes the spectrum. The algorithm is based on the fast Fourier transfo