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math.FA2012★ 1 cited
The Normal Defect of Some Classes of Matrices
Ryan D. Wasson, Hugo J. Woerdeman
An n \times n matrix A has a normal defect of k if there exists an (n+k) \times (n+k) normal matrix A_{ext} with A as a leading principal submatrix and k minimal. In this paper we…
math.FA2012
Norm-constrained determinantal representations of polynomials
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman
For every multivariable polynomial , with , we construct a determinantal representation where is a diagonal matrix with coordinate variables on…