Derivatives for antisymmetric tensor powers and perturbation bounds

In an earlier paper (R. Bhatia, T. Jain, Higher order derivatives and perturbation bounds for determinants, Linear Algebra Appl. 431 (2009) 2102–2108) we gave formulas for derivatives of all orders for the map that takes a matrix to its determinant. In this paper we continue that work, and find expressions for the derivatives of all orders for the antisymmetric tensor powers and for the coefficients of the characteristic polynomial. We then evaluate norms of these derivatives, and use them to obtain perturbation bounds.