Abstract
This chapter provides an overview of Birkhoff interpolation and some applications of coalescence. The method of the coalescence of two rows of a matrix was first used by D. Ferguson. The chapter discusses a simple proof of D. Ferguson's theorem describing the interpolation matrices that are complex regular For a Polya matrix E (1)δ (E) ≥ 0; (2) One has δ (E) > 0 if and only if one of the matrices of the canonical decomposition of E is non-Hermitian, with at least three nonzero rows. The chapter also discusses the theorem of Ferguson.
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