A={{1.2,3.7,5.6},{0,-2.2,4},{-5.3,0,1.4}}
{{1.2,3.7,5.6},{0,-2.2,4},{-5.3,0,1.4}}
MatrixForm[A]
1.2
3.7
5.6
0
-2.2
4
-5.3
0
1.4
Lam=Eigenvalues[A]
{2.0242+6.02601,2.0242-6.02601,-3.64839+0.}
P=Eigenvectors[A]
{{0.708621+0.,0.254522+0.220817,-0.063873+0.616631},{0.708621+0.,0.254522-0.220817,-0.063873-0.616631},{-0.308486+0.,0.8944+0.,-0.32386+0.}}
p=Transpose[P]
{{0.708621+0.,0.708621+0.,-0.308486+0.},{0.254522+0.220817,0.254522-0.220817,0.8944+0.},{-0.063873+0.616631,-0.063873-0.616631,-0.32386+0.}}
T=DiagonalMatrix[E^(Lam*t)]

(2.0242+6.02601)t

,0.,0.,0.,
(2.0242-6.02601)t

,0.,0.,0.,
(-3.64839+0.)t


X1=p.T.Inverse[p]
(-0.346075+0.)((0.+0.)-(0.308486+0.)
(-3.64839+0.)t

)+(0.630266-0.0255956)((0.+0.)+(0.708621+0.)
(2.0242-6.02601)t

)+(0.630266+0.0255956)((0.+0.)+(0.708621+0.)
(2.0242+6.02601)t

),(0.884069+0.)((0.+0.)-(0.308486+0.)
(-3.64839+0.)t

)+(0.192432+0.252093)((0.+0.)+(0.708621+0.)
(2.0242-6.02601)t

)+(0.192432-0.252093)((0.+0.)+(0.708621+0.)
(2.0242+6.02601)t

),(-0.316587+0.)((0.+0.)-(0.308486+0.)
(-3.64839+0.)t

)-(0.0689102-0.720582)((0.+0.)+(0.708621+0.)
(2.0242-6.02601)t

)-(0.0689102+0.720582)((0.+0.)+(0.708621+0.)
(2.0242+6.02601)t

),(-0.346075+0.)((0.+0.)+(0.8944+0.)
(-3.64839+0.)t

)+(0.630266-0.0255956)((0.+0.)+(0.254522-0.220817)
(2.0242-6.02601)t

)+(0.630266+0.0255956)((0.+0.)+(0.254522+0.220817)
(2.0242+6.02601)t

),(0.884069+0.)((0.+0.)+(0.8944+0.)
(-3.64839+0.)t

)+(0.192432+0.252093)((0.+0.)+(0.254522-0.220817)
(2.0242-6.02601)t

)+(0.192432-0.252093)((0.+0.)+(0.254522+0.220817)
(2.0242+6.02601)t

),(-0.316587+0.)((0.+0.)+(0.8944+0.)
(-3.64839+0.)t

)-(0.0689102-0.720582)((0.+0.)+(0.254522-0.220817)
(2.0242-6.02601)t

)-(0.0689102+0.720582)((0.+0.)+(0.254522+0.220817)
(2.0242+6.02601)t

),(-0.346075+0.)((0.+0.)-(0.32386+0.)
(-3.64839+0.)t

)+(0.630266-0.0255956)((0.+0.)-(0.063873+0.616631)
(2.0242-6.02601)t

)+(0.630266+0.0255956)((0.+0.)-(0.063873-0.616631)
(2.0242+6.02601)t

),(0.884069+0.)((0.+0.)-(0.32386+0.)
(-3.64839+0.)t

)+(0.192432+0.252093)((0.+0.)-(0.063873+0.616631)
(2.0242-6.02601)t

)+(0.192432-0.252093)((0.+0.)-(0.063873-0.616631)
(2.0242+6.02601)t

),(-0.316587+0.)((0.+0.)-(0.32386+0.)
(-3.64839+0.)t

)-(0.0689102-0.720582)((0.+0.)-(0.063873+0.616631)
(2.0242-6.02601)t

)-(0.0689102+0.720582)((0.+0.)-(0.063873-0.616631)
(2.0242+6.02601)t

)
MatrixForm[FullSimplify[X1]]
0.106759
-3.64839t

+(0.44662-0.0181376)
(2.0242-6.02601)t

+(0.44662+0.0181376)
(2.0242+6.02601)t

-0.272723
-3.64839t

+(0.136361+0.178639)
(2.0242-6.02601)t

+(0.136361-0.178639)
(2.0242+6.02601)t

0.0976625
-3.64839t

-(0.0488312-0.51062)
(2.0242-6.02601)t

-(0.0488312+0.51062)
(2.0242+6.02601)t

-0.30953
-3.64839t

+(0.154765-0.145688)
(2.0242-6.02601)t

+(0.154765+0.145688)
(2.0242+6.02601)t

0.790711
-3.64839t

+(0.104645+0.0216712)
(2.0242-6.02601)t

+(0.104645-0.0216712)
(2.0242+6.02601)t

-0.283155
-3.64839t

+(0.141577+0.198621)
(2.0242-6.02601)t

+(0.141577-0.198621)
(2.0242+6.02601)t

0.11208
-3.64839t

-(0.0560401+0.387007)
(2.0242-6.02601)t

-(0.0560401-0.387007)
(2.0242+6.02601)t

-0.286315
-3.64839t

+(0.143157-0.134761)
(2.0242-6.02601)t

+(0.143157+0.134761)
(2.0242+6.02601)t

0.10253
-3.64839t

+(0.448735-0.00353355)
(2.0242-6.02601)t

+(0.448735+0.00353355)
(2.0242+6.02601)t
