A matrix completion problem over integral domainsthe case with 2n — 3 prescribed blocks

  1. Borobia, Alberto 1
  2. Canogar, Roberto 1
  3. Smigoc, Helena 2
  1. 1 Universidad Nacional de Educación a Distancia
    info

    Universidad Nacional de Educación a Distancia

    Madrid, España

    ROR https://ror.org/02msb5n36

  2. 2 University College Dublin.
Revista:
Proyecciones: Journal of Mathematics

ISSN: 0716-0917,  0717-6279

Año de publicación: 2014

Volumen: 33

Número: 2

Páginas: 215-233

Tipo: Artículo

DOI: 10.4067/S0716-09172014000200007 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Proyecciones: Journal of Mathematics

Resumen

Let ∧ = {λ1,...,λnk} be amultisetofelements ofanintegral domain R.Let P be a partially prescribed n X n block matrix such that each prescribed entry is a k—block (a k X k matrix over R). If P has at most 2n — 3 prescribed entries then the unprescribed entries of P can be filled with k—blocks to obtain a matrix over R with spectrum ∧ (some natural conditions on the prescribed entries are required). We describe an algorithm to construct such completion.

Referencias bibliográficas

  • Citas [1] A. Borobia, Inverse eigenvalue problems, in: Leslie Hogben (Ed.), Handbook of linear algebra, 2nd edition, Discrete Mathematics and its Applications, Chapman and Hall/CRC, to appear (chapter 28).
  • [2] A. Borobia and R. Canogar. Matrix completion problem over integral domains: the case with a diagonal of prescribed blocks. Lin. Alg. Appl., 436(1): pp. 222—236, (2012).
  • [3] A. Borobia, R. Canogar, and H. Smigoc. A matrix completion problem over integral domains: the case with 2n-3 prescribed entries. Lin. Alg. Appl., 433: pp. 606—617, (2010).
  • [4] Moody T. Chu, Fasma Diele, and Ivonne Sgura. Gradient flow methods for matrix completion with prescribed eigenvalues. Linear Algebra Appl., 379: pp. 85—112, (2004). Tenth Conference of the International Linear Algebra Society.
  • [5] Moody T. Chu and Gene H. Golub. Inverse eigenvalue problems: theory, algorithms, and applications. Numerical Mathematics and Scientific Computation. Oxford University Press, New York, (2005).
  • [6] G. Cravo and F.C. Silva. Eigenvalues of matrices with several prescribed blocks. Lin. Alg. Appl., 311: pp. 13—24, (2000).
  • [7] D. Hershkowitz. Existence of matrices with prescribed eigenvalues and entries. Linear and Multilinear Algebra, 14(4): pp. 315—342, (1983).
  • [8] Kh.D. Ikramov and V.N. Chugunov. Inverse matrix eigenvalue problems. J. Math. Sci. (New York), 98(1): pp. 51—136, (2000).
  • [9] Helena Smigoc. The inverse eigenvalue problem for nonnegative matrices. Linear Algebra Appl., 393: pp. 365—374, (2004).
Fuente de los datos: Dialnet