A generalization of Mü hlbach's extension principle for determinantal identities

摘要

Mü hlbach's extension principle for determinantal identities generalizes Muir's law of extensible minors. Some particular issues with Mü hlbach– Beckermann's identity [A general determinantal identity of Sylvester type and some applications, Linear Algebra Appl. 197, 198 (1994), pp. 93–112] led to the conjecture of a more general extension method than Mü hlbach's. However, no confirmation seems to have been reported so far. In this note, we present a generalization of Mü hlbach's extension principle which confirms that conjecture. The whole identity of Mü hlbach–Beckermann is put in a simpler form from which a new interpretation as an extension of Leibniz's definition of a determinant.