n’th derivative of a determinant

Let A=(ai,j) be a d×d matrix whose entries are real functions of t. Then,


where (nn1,n2,,nr) is the multinomial coefficientDlmfMathworldPlanetmath, Sd is the symmetric groupMathworldPlanetmathPlanetmath of permutationsMathworldPlanetmath and sgn(π) is the sign of a permutation π.

Title n’th derivative of a determinant
Canonical name NthDerivativeOfADeterminant
Date of creation 2013-03-22 14:30:25
Last modified on 2013-03-22 14:30:25
Owner GeraW (6138)
Last modified by GeraW (6138)
Numerical id 5
Author GeraW (6138)
Entry type Result
Classification msc 15A15
Related topic GeneralizedLeibnizRule
Related topic MultinomialTheorem
Related topic DerivativeOfMatrix