Why am I getting an incorrect result from multiplying an inverted matrix by a vector?

Question

I’m trying to learn Python for basic work in linear algebra. I’m running into the following problem with a simple system of linear equations:

import scipy.linalg as la
import numpy as np

A = np.array([[186/450, 54/21, 30/60],
              [12/450,  6/21 ,  3/60],
              [9/450,   6/21 , 15/60]])
l = np.array([18/450, 12/21, 30/36])
b = np.array([2, 0, 1/6])
y = np.array([180, 0, 30])
x = la.inv(np.eye(3) - A) @ y

lam = np.transpose(l) @ la.inv(np.eye(3) - A)

This returns

array([0.21212121, 2.12121212, 1.39393939])

which is incorrect. Performing the same operation in Julia,

A = [186/450 54/21 30/60;
     12/450 6/21 3/60;
     9/450 6/21 15/60]
l = [18/450, 12/21, 30/60]
b = [2, 0, 1/6]
y = [180, 0, 30]
 
λ = l' * inv(I - A)

yields the correct result, which is

1×3 adjoint(::Vector{Float64}) with eltype Float64:
 0.181818  1.81818  0.909091

What am I missing here? I think I might be missing something in the opaque numpy array syntax.

Asked By: skinamarink

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Source

Answer 1

There is a typo in l instantiation in your python code. (30/36 should be 30/60).

This code with the typo fixed produces the same result as in Julia.

import scipy.linalg as la
import numpy as np

A = np.array([[186/450, 54/21, 30/60],
              [12/450,  6/21 ,  3/60],
              [9/450,   6/21 , 15/60]])
l = np.array([18/450, 12/21, 30/60]) #typo fixed here
b = np.array([2, 0, 1/6])
y = np.array([180, 0, 30])
x = la.inv(np.eye(3) - A) @ y

lam = np.transpose(l) @ la.inv(np.eye(3) - A)

Giving:

array([0.18181818, 1.81818182, 0.90909091])

Answered By: Ryan Marizza

Why am I getting an incorrect result from multiplying an inverted matrix by a vector?

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