Differential calculus for p-norms, differential calculus for vector norms, Applied Mathematics, Numerical computation of matrix norms, conditioning, scaling, Systems arising from the discretization of structural vibration problems, norm of a vector function, error bounds, Nonlinear ordinary differential equations and systems, Best upper bound, Application to vibration problem, Computational Mathematics, Right derivative, Right derivative of the norm of a vector function, right derivative, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Differential calculus for vector norms, vibration problem, Vector and tensor algebra, theory of invariants, Error bounds for numerical methods for ordinary differential equations