Matrix Polynomials and Power Series

Matrices can be used in infinite series, such as tlte exponential, trigonometric, and logarithmic series. For example, the matrix exponential lunction is defined as 

Note that in MATLAB, the functions exp(A), c. o.r(A), sin A), are element-by-element functions and do not obey the above definitions. The MATLAB functions expm A), expmJ A), expm2 A), and expmSiA) calculate exponential of the matrix A by different algorithms. The function expm2(A) calculates exponential of the matrix A as in Eq. (2.83). 

---