A generalization of Muhlbach's extension principle for determinantal identities

作者：de Camargo Andre Pierro^*

来源：Linear and Multilinear Algebra, 2013, 61(10): 1363-1376.

DOI：10.1080/03081087.2012.740028

• determinantal identities
• law of extensible minors
• Gaussian elimination
• Sylvester's identity

Muhlbach's extension principle for determinantal identities generalizes Muir's law of extensible minors. Some particular issues with Muhlbach-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 Muhlbach's. However, no confirmation seems to have been reported so far. In this note, we present a generalization of Muhlbach's extension principle which confirms that conjecture. The whole identity of Muhlbach-Beckermann is put in a simpler form from which a new interpretation as an extension of Leibniz's definition of a determinant.

• 出版日期2013-10-1