Abstract
We discuss the problem of completing a partially specified matrix \( \left[ {\begin{array}{*{20}c}A \\C \\\end{array} {\text{ }}\begin{array}{*{20}c}B \\? \\\end{array} } \right] \) subject to a bound on the rnth singular value. A complete solution was given by Arsene, Constantinescu, and Gheondea [ACG]. We present a more elementary approach appropriate to the matrix case based on the use of Möbius transformations.
Dedicated to Israel Gohberg with affection and esteem
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Ogle, D., Young, N. (2001). The Parrott Problem for Singular Values. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_22
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DOI: https://doi.org/10.1007/978-3-0348-8323-8_22
Publisher Name: Birkhäuser, Basel
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