March 18, 2013 at 12:24 - by eelvex | no comments (Leave a comment)

For the well behaved matrices of quantum mechanics, it's simply:

matexp(A) = {

P = mateigen(A);

(P*matdiagonal(exp(polroots(charpoly(A))))*matadjoint(P))/matdet(P)

}

P = mateigen(A);

(P*matdiagonal(exp(polroots(charpoly(A))))*matadjoint(P))/matdet(P)

}

using the fact that where are A's eigenvalues and P is the matrix of eigenvectors of A.

For example

matexp([1,2;3,4])

[51.968956198705003658124484242647420628 + 0.E-37*I 74.736564567003212549882577707218180515 + 0.E-37*I]

[112.10484685050481882482386656082727077 + 0.E-36*I 164.07380304920982248294835080347469140 + 0.E-36*I]

[51.968956198705003658124484242647420628 + 0.E-37*I 74.736564567003212549882577707218180515 + 0.E-37*I]

[112.10484685050481882482386656082727077 + 0.E-36*I 164.07380304920982248294835080347469140 + 0.E-36*I]

Wolfram alpha agrees:

(51.969 | 74.7366

112.105 | 164.074)

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