Hi Kaitlin,
It seems like the message is due to an underlying call to JordanDecomposition, which doesn't like the approximate numeric value (-1.02) in your input matrix. I'm not sure why off the top of my head. There are others here who are more knowledgeable and who could probably explain.
If you Rationalize your input matrix (converting the approximate number to the exact rational -102/100), you can avoid the message. The reason this works is likely that a wholly symbolic/exact matrix allows for use of a different internal method in MatrixExp or JordanDecomposition.
FsA =
10*{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-(0.102)*s^2, 0, 0, 0}}
(* Out:
{{0, 10, 0, 0}, {0, 0, 10, 0}, {0, 0, 0, 10}, {-1.02 s^2, 0,
0, 0}}
*)
FsASet = MatrixExp[Rationalize[FsA]]
(* Out:
{{1/
2 E^(-255^(1/4) Sqrt[s]) (1 + E^(2 255^(1/4) Sqrt[s])) Cos[
255^(1/4) Sqrt[s]], (1/(2 51^(1/4) Sqrt[s]))
5^(3/4) E^(-255^(1/4) Sqrt[
s]) (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] +
Sin[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]]), (
5 Sqrt[5/51]
E^(-255^(1/4) Sqrt[s]) (-1 + E^(2 255^(1/4) Sqrt[s])) Sin[
255^(1/4) Sqrt[s]])/
s, -(1/(51^(3/4) s^(3/2)))
25 5^(1/4)
E^(-255^(1/4) Sqrt[
s]) (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] -
Sin[255^(1/4) Sqrt[s]] -
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]])}, {(1/(
4 5^(3/4)))
51^(1/4) E^(-255^(1/4) Sqrt[s]) Sqrt[
s] (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] -
Sin[255^(1/4) Sqrt[s]] -
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]]),
1/2 E^(-255^(1/4) Sqrt[s]) (1 + E^(2 255^(1/4) Sqrt[s])) Cos[
255^(1/4) Sqrt[s]], (1/(2 51^(1/4) Sqrt[s]))
5^(3/4) E^(-255^(1/4) Sqrt[
s]) (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] +
Sin[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]]), (
5 Sqrt[5/51]
E^(-255^(1/4) Sqrt[s]) (-1 + E^(2 255^(1/4) Sqrt[s])) Sin[
255^(1/4) Sqrt[s]])/
s}, {-(1/20) Sqrt[51/5]
E^(-255^(1/4) Sqrt[s]) (-1 + E^(2 255^(1/4) Sqrt[s])) s Sin[
255^(1/4) Sqrt[s]], (1/(4 5^(3/4)))
51^(1/4) E^(-255^(1/4) Sqrt[s]) Sqrt[
s] (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] -
Sin[255^(1/4) Sqrt[s]] -
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]]),
1/2 E^(-255^(1/4) Sqrt[s]) (1 + E^(2 255^(1/4) Sqrt[s])) Cos[
255^(1/4) Sqrt[s]], (1/(2 51^(1/4) Sqrt[s]))
5^(3/4) E^(-255^(1/4) Sqrt[
s]) (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] +
Sin[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]])}, {-(1/(
200 5^(1/4)))
51^(3/4) E^(-255^(1/4) Sqrt[s]) s^(
3/2) (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] +
Sin[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]]), -(1/20) Sqrt[
51/5] E^(-255^(1/4) Sqrt[s]) (-1 + E^(2 255^(1/4) Sqrt[s])) s Sin[
255^(1/4) Sqrt[s]], (1/(4 5^(3/4)))
51^(1/4) E^(-255^(1/4) Sqrt[s]) Sqrt[
s] (-Cos[255^(1/4) Sqrt[s]] +
E^(2 255^(1/4) Sqrt[s]) Cos[255^(1/4) Sqrt[s]] -
Sin[255^(1/4) Sqrt[s]] -
E^(2 255^(1/4) Sqrt[s]) Sin[255^(1/4) Sqrt[s]]),
1/2 E^(-255^(1/4) Sqrt[s]) (1 + E^(2 255^(1/4) Sqrt[s])) Cos[
255^(1/4) Sqrt[s]]}}
*)
FsASetx = MatrixExp[Rationalize[FsA x]]
(* Out:
{{1/
2 E^(-255^(1/4) Sqrt[s] x) (1 + E^(2 255^(1/4) Sqrt[s] x)) Cos[
255^(1/4) Sqrt[s] x], (1/(2 51^(1/4) Sqrt[s]))
5^(3/4) E^(-255^(1/4) Sqrt[s]
x) (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] +
Sin[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x]), (
5 Sqrt[5/51]
E^(-255^(1/4) Sqrt[s] x) (-1 + E^(2 255^(1/4) Sqrt[s] x)) Sin[
255^(1/4) Sqrt[s] x])/
s, -(1/(51^(3/4) s^(3/2)))
25 5^(1/4)
E^(-255^(1/4) Sqrt[s]
x) (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] -
Sin[255^(1/4) Sqrt[s] x] -
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x])}, {(1/(
4 5^(3/4)))
51^(1/4) E^(-255^(1/4) Sqrt[s] x) Sqrt[
s] (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] -
Sin[255^(1/4) Sqrt[s] x] -
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x]),
1/2 E^(-255^(1/4) Sqrt[s] x) (1 + E^(2 255^(1/4) Sqrt[s] x)) Cos[
255^(1/4) Sqrt[s] x], (1/(2 51^(1/4) Sqrt[s]))
5^(3/4) E^(-255^(1/4) Sqrt[s]
x) (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] +
Sin[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x]), (
5 Sqrt[5/51]
E^(-255^(1/4) Sqrt[s] x) (-1 + E^(2 255^(1/4) Sqrt[s] x)) Sin[
255^(1/4) Sqrt[s] x])/
s}, {-(1/20) Sqrt[51/5]
E^(-255^(1/4) Sqrt[s] x) (-1 + E^(2 255^(1/4) Sqrt[s] x)) s Sin[
255^(1/4) Sqrt[s] x], (1/(4 5^(3/4)))
51^(1/4) E^(-255^(1/4) Sqrt[s] x) Sqrt[
s] (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] -
Sin[255^(1/4) Sqrt[s] x] -
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x]),
1/2 E^(-255^(1/4) Sqrt[s] x) (1 + E^(2 255^(1/4) Sqrt[s] x)) Cos[
255^(1/4) Sqrt[s] x], (1/(2 51^(1/4) Sqrt[s]))
5^(3/4) E^(-255^(1/4) Sqrt[s]
x) (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] +
Sin[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x])}, {-(1/(
200 5^(1/4)))
51^(3/4) E^(-255^(1/4) Sqrt[s] x) s^(
3/2) (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] +
Sin[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x]), -(1/20)
Sqrt[51/5]
E^(-255^(1/4) Sqrt[s] x) (-1 + E^(2 255^(1/4) Sqrt[s] x)) s Sin[
255^(1/4) Sqrt[s] x], (1/(4 5^(3/4)))
51^(1/4) E^(-255^(1/4) Sqrt[s] x) Sqrt[
s] (-Cos[255^(1/4) Sqrt[s] x] +
E^(2 255^(1/4) Sqrt[s] x) Cos[255^(1/4) Sqrt[s] x] -
Sin[255^(1/4) Sqrt[s] x] -
E^(2 255^(1/4) Sqrt[s] x) Sin[255^(1/4) Sqrt[s] x]),
1/2 E^(-255^(1/4) Sqrt[s] x) (1 + E^(2 255^(1/4) Sqrt[s] x)) Cos[
255^(1/4) Sqrt[s] x]}}
*)