|MATLAB Function Reference|
L = logm(A)
is the principal matrix logarithm of A, the inverse of
L is the unique logarithm for which every eigenvalue has imaginary part lying strictly between - and . If
A is singular or has any eigenvalues on the negative real axis, the principal logarithm is undefined. In this case,
logm computes a non-principal logarithm and returns a warning message.
[L, exitflag] = logm(A) returns a scalar
exitflag that describes the exit condition of
exitflag = 0, the algorithm was successfully completed.
exitflag = 1, one or more Taylor series evaluations did not converge. However, the computed value of
Lmight still be accurate.
A can have class
A is real symmetric or complex Hermitian, then so is
Some matrices, like
A = [0 1; 0 0], do not have any logarithms, real or complex, so
logm cannot be expected to produce one.
For most matrices:
These identities may fail for some
A. For example, if the computed eigenvalues of
A include an exact zero, then
logm(A) generates infinity. Or, if the elements of
A are too large,
expm(A) may overflow.
A is the 3-by-3 matrix
A = logm(Y) produces the original matrix
log(A) involves taking the logarithm of zero, and so produces
logm uses is described in .
 Davies, P. I. and N. J. Higham, "A Schur-Parlett algorithm for computing matrix functions," SIAM J. Matrix Anal. Appl., Vol. 25, Number 2, pp. 464-485, 2003.
 Cheng, S. H., N. J. Higham, C. S. Kenney, and A. J. Laub, "Approximating the logarithm of a matrix to specified accuracy," SIAM J. Matrix Anal. Appl., Vol. 22, Number 4, pp. 1112-1125, 2001.
 Higham, N. J., "Evaluating Pade approximants of the matrix logarithm," SIAM J. Matrix Anal. Appl., Vol. 22, Number 4, pp. 1126-1135, 2001.
 Golub, G. H. and C. F. Van Loan, Matrix Computation, Johns Hopkins University Press, 1983, p. 384.
 Moler, C. B. and C. F. Van Loan, "Nineteen Dubious Ways to Compute the Exponential of a Matrix," SIAM Review 20, 1979,pp. 801-836.
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