Abstract
In this paper, the local evaluation of the derivative of a determinant of a λ-matrix is considered. The entries of a λ-matrix are scalar polynomials, of finite degree, in the independent variable λ. The existing methods with O ( N 3 ) operation counts; developed for non-singular matrices, are reviewed, and extended, where possible, to singular matrices. An alternative approach, similar in nature to the previous methods, based on direct selection of the necessary matrix entries, is suggested. A general expression, valid at both singular and non-singular points, is derived and then the simplifications to be found in special cases are discussed, and applications where the algorithms might be useful are given.
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