# The schwerdtfeger formula to calculate functions of matrices

#### Abstract

This thesis shows an extension of the Schwerdtfeger formula to calculate the maps t to f(tA) for a given matrix A and a holomorphic function f. The main result shows that the computational cost of the new formula is the same as the original due to Schwerdtfeger. This allows one to explicitly calculate the maps t to exp(tA), t to cos(tA), and t to sin(tA) (among others) provided the spectrum of A is known.^

#### Subject Area

Applied Mathematics|Mathematics

#### Recommended Citation

Earnest III Anthony,
"The schwerdtfeger formula to calculate functions of matrices"
(2013).
*ETD Collection for Tennessee State University.*
Paper AAI1547712.

https://digitalscholarship.tnstate.edu/dissertations/AAI1547712