Matrix Index Matrix Exponentials

Transfer: https://zh.wikipedia.org/wiki/%E7%9F%A9%E9%98%B5%E6%8C%87%E6%95%B0

 

Wherein, X-, X- ² , X- ^{. 3} ...... , X- ^K  is the matrix of order n, apparently exp (X) is also a matrix of order n, power series expansion must be convergent , so that exp (X) although particularly inconvenient hand calculated value , but it does an analytic expression ;

 

Role in the solution matrix index ode in:

ODE is actually variable separable, by solving the separation of variables , and is expressed in the form of a matrix index

 

 Analytical solution matrix index calculation is a point of discussion in mathematical research, there are currently only for the special nature / mature form of a matrix solution;

 

You can use the MATLAB expm (), logM () function is approximated