MATLAB Function Reference 
Syntax
Description
Y = expm(X)
raises the constant to the matrix power X
. The expm
function produces complex results if X
has nonpositive eigenvalues.
Use exp
for the elementbyelement exponential.
Algorithm
expm
is a builtin function that uses the Padé approximation with scaling and squaring. You can see the coding of this algorithm in the expm1
demo.
Note
The expm1 , expm2 , and expm3 demos illustrate the use of Padé approximation, Taylor series approximation, and eigenvalues and eigenvectors, respectively, to compute the matrix exponential.References [1] and [2] describe and compare many algorithms for computing a matrix exponential. The builtin method, expm , is essentially method 3 of [2].

Examples
This example computes and compares the matrix exponential of A
and the exponential of A
.
A = [1 1 0 0 0 2 0 0 1 ];expm(A)
ans = 2.7183 1.7183 1.0862 0 1.0000 1.2642 0 0 0.3679exp(A)
ans = 2.7183 2.7183 1.0000 1.0000 1.0000 7.3891 1.0000 1.0000 0.3679
Notice that the diagonal elements of the two results are equal. This would be true for any triangular matrix. But the offdiagonal elements, including those below the diagonal, are different.
See Also
References
[1] Golub, G. H. and C. F. Van Loan, Matrix Computation, p. 384, Johns Hopkins University Press, 1983.
[2] Moler, C. B. and C. F. Van Loan, "Nineteen Dubious Ways to Compute the Exponential of a Matrix," SIAM Review 20, 1979, pp. 801836.
expint  eye 