- #1
juaninf
- 27
- 0
How can prove this
[tex]\exp(At)\exp(-At_0)=\exp(A(t-t_0))[/tex]?
using [tex]\displaystyle\sum_{i=0}^n{(1/k!)A^kt^k}[/tex]
and this properties
in t=0
[tex]
[\exp(At)]_{t} = I
[/tex][tex]exp(At)exp(-At)=I[/tex]
[tex]\frac{dexp(At)}{dt}=Aexp(At)=exp(At)A[/tex]
[tex]\exp(At)\exp(-At_0)=\exp(A(t-t_0))[/tex]?
using [tex]\displaystyle\sum_{i=0}^n{(1/k!)A^kt^k}[/tex]
and this properties
in t=0
[tex]
[\exp(At)]_{t} = I
[/tex][tex]exp(At)exp(-At)=I[/tex]
[tex]\frac{dexp(At)}{dt}=Aexp(At)=exp(At)A[/tex]
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