Inverse of a matrix in SymPy?

Question

I was wondering how to create a matrix and compute its inverse using SymPy in Python?

For example, for this symbolic matrix:

Solution 1

If your question was: How to compute the inverse of a matrix M in sympy then:

M_inverse = M.inv()

As for how to create a matrix:

M = Matrix(2,3, [1,2,3,4,5,6])

will give you the following 2X3 matrix:

1 2 3

4 5 6

See: http://docs.sympy.org/0.7.2/modules/matrices/matrices.html

Solution 2

Here is example of how we can compute inverse for a symbolic matrix (taking the one from the question):

import sympy as sym


# Not necessary but gives nice-looking latex output
# More info at: http://docs.sympy.org/latest/tutorial/printing.html
sym.init_printing()

sx, sy, rho = sym.symbols('sigma_x sigma_y rho')
matrix = sym.Matrix([[sx ** 2, rho * sx * sy], 
                     [rho * sx * sy, sy ** 2]])

Now printing the inverse matrix.inv() will give:
                                      

which can be further simplified like sym.simplify(matrix.inv()):
                                                

Comments

[Karlo]

What is the difference between M.inv() and Inverse(M)?

[yokke]

@Karlo I'm not sure, if related, but have a look: stackoverflow.com/questions/50854803/…