- #1
- 1,283
- 1,096
Let ##A(t)## be an ##m \times m## matrix continuously dependent on ##t \in \mathbb{R},##
and let X be the fundamental matrix satisfying
$$\dot X = A(t)X, \quad X(0) = E.$$
In the text attached below it is shown that Liouville's formula
$$\det X(t) = e^{\int_0^t \mathrm{tr} A(s) ds},$$
is a direct consequence of several other general and fundamental facts.
and let X be the fundamental matrix satisfying
$$\dot X = A(t)X, \quad X(0) = E.$$
In the text attached below it is shown that Liouville's formula
$$\det X(t) = e^{\int_0^t \mathrm{tr} A(s) ds},$$
is a direct consequence of several other general and fundamental facts.