Chapter 17
Functions of Matrices
Nicholas J. Higham
University of Manchester
Matrix functions are used in many areas of linear algebra and arise in numerous applications in science and engineering. The most common matrix function is the matrix inverse; it is not treated specifically in this chapter, but is covered in Section 1.5 and Section 51.3. This chapter is concerned with general matrix functions as well as specific cases such as matrix square roots, trigonometric functions, and the exponential and logarithmic functions.
The specific functions just mentioned can all be defined via power series or as the solution of nonlinear systems. For example, cos(A) = I − A2/2! + A4/4! −.... However, a general theory exists from which a number of properties ...
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