In [1]:

    

import numpy as np
import sympy as sp


    

In [26]:

    

a,b,c,d = sp.symbols('a, b, c, d')
w = sp.symbols('w')
s = sp.symbols('s')
h = sp.symbols('h')
A = sp.Matrix([[0, w], [-w, 0]])
I2 = sp.Matrix([[1, 0], [0, 1]])
B = sp.Matrix([[a,b],[c,d]])
B.inv()


    

    
Out[26]:





Matrix([
[1/a + b*c/(a**2*(d - b*c/a)), -b/(a*(d - b*c/a))],
[          -c/(a*(d - b*c/a)),      1/(d - b*c/a)]])

In [21]:

    

As = (s*I2-A)
As


    

    
Out[21]:





Matrix([
[s, -w],
[w,  s]])

In [22]:

    

Asinv = As.inv()
sp.pretty_print(Asinv)


    

    




⎡          2                ⎤
⎢1        w           w     ⎥
⎢─ - ───────────  ──────────⎥
⎢s      ⎛     2⎞    ⎛     2⎞⎥
⎢     2 ⎜    w ⎟    ⎜    w ⎟⎥
⎢    s ⋅⎜s + ──⎟  s⋅⎜s + ──⎟⎥
⎢       ⎝    s ⎠    ⎝    s ⎠⎥
⎢                           ⎥
⎢     -w              1     ⎥
⎢  ──────────       ──────  ⎥
⎢    ⎛     2⎞            2  ⎥
⎢    ⎜    w ⎟           w   ⎥
⎢  s⋅⎜s + ──⎟       s + ──  ⎥
⎣    ⎝    s ⎠           s   ⎦

In [18]:

    

sp.LaplaceTransform?


    

In [6]:

    

A*A*A


    

    
Out[6]:





Matrix([
[   0, -w**3],
[w**3,     0]])

In [ ]:

    

As =