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

Alberto Borobia, Roberto Canogar, Helena Smigoc

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.

Palabras clave


Matrix completions; inverse eigenvalue problems; matrices over integral domains; completación de matrices; problemas de valor propio inverso; matrices sobre dominios integrales.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172014000200007

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