def test_basis_creation():
assert Vector.basis(0, 2) == Vector(1, 0)
assert Vector.basis(3, 6) == Vector(0, 0, 0, 1, 0, 0)
def test_vector_splitting_to_basis_products():
product_vector = Vector.zero(len(a))
for i, component in enumerate(a):
product_vector += Vector.basis(i, len(a)) * component
assert product_vector == a
def identity(cls, m: int) -> 'Matrix':
"""
Returns the identity matrix m by m
"""
return cls(rows=(Vector.basis(i, m) for i in range(m)))