matlog: Matrix Logarithm
In complexplus: Functions of Complex or Real Variable

Description Usage Arguments Details Value Author(s) References See Also Examples

matlog computes the (principal) matrix logarithm of a square matrix.

1	matlog(A, ...)

`A`	a square matrix, real or complex.
`...`	arguments passed to or from other methods.

This function adapts function logm from package expm to be able to handle complex matrices, by decomposing the original matrix into real and purely imaginary matrices and creating a real block matrix that function logm can successfully process. If the original matrix is real, matlog calls logm directly for maximum efficiency. Hence, for real matrices, matlog can compute the matrix logarithm in the same instances as logm; for complex matrices, matlog can compute the matrix logarithm as long as all real eigenvalues are positive: zero eigenvalues imply singularity (and therefore the log does not exist) and negative eigenvalues can be problematic as it may be hard and numerically unstable to calculate Jordan blocks. See references below.

The matrix logarithm of A. Method used may be chosen from the options available in logm.

Albert Dorador

For more on the matrix logarithm, visit https://en.wikipedia.org/wiki/Logarithm_of_a_matrix

logm

A <- matrix(c(1, 2, 2+3i, 5), ncol = 2)  # complex matrix
B <- matrix(c(2, 0, 3, 4), ncol = 2)  # real matrix with positive eigenvalues

matlog(A)
matlog(A, "Eigen")  # uses Eigen method in function logm
matlog(B)
matlog(B, "Eigen")  # uses Eigen method in function logm