6.1 Nonlinear computation of matrix elements6.1.1 Integer rounding and rationalization6.1.2 Transcendental function computations6.1.3 Vector sorting, minimization, and maximization6.1.4 Means, variances, and standard deviations6.2 Matrix exponentials6.2.1 Definitions and properties of matrix functions6.2.2 Computing matrix exponentials6.2.3 Taylor series-based truncation algorithm6.2.4 A Cayley–Hamilton theorem-based algorithm6.2.5 Direct MATLAB solver6.2.6 Jordan transform-based approach6.3 Matrix logarithmic and square root functions6.3.1 Matrix logarithmic function6.3.2 Square root of a matrix6.4 Matrix trigonometric functions6.4.1 Computation of matrix trigonometric functions6.4.2 Power series-based trigonometric function evaluation6.4.3 Analytical evaluations of matrix trigonometric functions6.5 Arbitrary matrix functions6.5.1 Nilpotent matrices6.5.2 Jordan transform-based matrix function evaluations6.5.3 User-defined matrix functions6.6 Matrix powers6.6.1 Matrix powers via Jordan transform6.6.2 A matrix power solver6.6.3 Matrix powers via the z transform6.6.4 Computing kA6.7 Problems