4.1.1 Vectors and matrices

Creating vectors is as simple as using the function array to convert a list into an array:

v = array([1.,2.,3.])

The object v is now a vector that behaves much like a vector in linear algebra. We have already emphasized the differences with the list object in Python in Section 3.2: A quick glance at the concept of arrays.

Here are some illustrations of the basic linear algebra operations on vectors:

# two vectors with three components
v1 = array([1., 2., 3.])
v2 = array([2, 0, 1.])

# scalar multiplications/divisions
2*v1 # array([2., 4., 6.])
v1/2 # array([0.5, 1., 1.5])

# linear combinations
3*v1 # array([ 3., 6., 9.])
3*v1 + 2*v2 # array([ 7., 6., 11.])

# norm
from numpy.linalg import norm
norm(v1) # 3.7416573867739413
# scalar product
dot(v1, v2) # 5.0
v1 @ v2 # 5.0 ; alternative formulation

Note that all basic arithmetic operations are performed elementwise:

# elementwise operations:
v1 * v2 # array([2., 0...