Functions of Diagonalizable Matrices

Equations A.5.17 and A.5.20 may be used for computing polynomials and functions of diagonalizable matrices of any order ( m) with m distinct eigenvalues (A (Lancaster and Tismenetsky, 1985). 

Functions of a diagonalizable matrix can be evaluated by an alternative procedure. If [A] represents a diagonal matrix 

In general, we can evaluate any function of a diagonalizable matrix [yl] by the above procedure. Thus, 

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