A matrix completion problem over integral domains: the case with 2n — 3 prescribed blocks

  • Alberto Borobia UNED.
  • Roberto Canogar UNED.
  • Helena Smigoc University College Dublin.
Palabras clave: Matrix completions, inverse eigenvalue problems, matrices over integral domains, completación de matrices, problemas de valor propio inverso, matrices sobre dominios integrales.


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.

Biografía del autor

Alberto Borobia, UNED.
Departamento Matemáticas.
Roberto Canogar, UNED.
Departamento Matemáticas.
Helena Smigoc, University College Dublin.
School of Mathematical Sciences.


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Cómo citar
Borobia, A., Canogar, R., & Smigoc, H. (2017). A matrix completion problem over integral domains: the case with 2n — 3 prescribed blocks. Proyecciones. Journal of Mathematics, 33(2), 215-233. https://doi.org/10.4067/S0716-09172014000200007