Python multiplying float

Question

I'm trying to check if matrix of orthonormal by multiplying matrix with transpose itself.

import numpy as np
matrix = np.array([[np.sqrt(2)/2, -np.sqrt(2)/2],
 [np.sqrt(2)/2, np.sqrt(2)/2]])
dot = matrix.T.dot(matrix)
print(dot)

Expected output

[[1. 0.]
 [0. 1.]]

Instead of that, I got

[[ 1.00000000e+00 -4.26642159e-17]
 [-4.26642159e-17 1.00000000e+00]]

I've tried to use different types: float64, float128, complex128. But answer is still incorrect.

• sushanth: dot.round(2)
• user2357112: Up to rounding error, -4.26642159e-17 is 0. The e-17 on the end means "times 10 to the power of -17".
• Eric Postpischil: (a) The matrix is not orthonormal, because np.sqrt(2)/2 is not exactly the square root of two; it has an error due to rounding to the floating-point format. So the test is correctly telling you that the matrix is not orthonormal. You can test whether it is near orthonormal, possibly by testing whether the product of the matrix and its transpose is near the identity matrix. But then (b) you have to define how near is acceptable, as well as defining a metric for "near," and (c) you have to accept that the test will report some non-orthonormal matrices as orthonormal.

Answer 1

That comes from python dividing numbers. This is done in the binary, which produces such a result. You are looking for round() function

matrix = np.array([[round(np.sqrt(2)/2, 2), round(-np.sqrt(2)/2, 2)],
 [round(np.sqrt(2)/2, 2), round(np.sqrt(2)/2), 2]])

• sushanth: Looks like there is some syntax errror.
• Aleksander Ikleiw: @Sushanth thank you for pointing, I have made a typo - I am writing from the phone and did not see that I missed the ]
• user2357112: You're rounding the wrong matrix (and the choice to round to 2 digits after the decimal point is arbitrary and unexplained).
• user2357112: Your parentheses are wrong on the last round call (and you're still rounding the wrong matrix).