Explicit formulas to calculate MV functions in a basis-free
representation are presented for an arbitrary Clifford geometric algebra
Cl p , q . The formulas are based on analysis of the roots of minimal MV
polynomial and covers defective MVs, i.e. the MVs that have
non-diagonalizable matrix representations. The method may be generalized
straightforwardly to matrix functions and to finite dimensional linear
operators. The results can find wide application in Clifford algebra
analysis.