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>>> import numpy as np

>>> # Scalars are just a single number.
>>> scalar = 5.0
>>> np.isscalar(scalar)
True

>>> # Vectors are a matrix with one column.
>>> vector = np.arange(10)
>>> vector

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>>> import numpy as np

>>> # Create a random matrix with 3 rows and 4 columns.
>>> matrix_a = np.random.random_sample((3, 4))
>>> matrix_a
array([[ 0.21922347,  0.84313988,  0.41381942,  0.53553901],
       [ 0.35322431,  0.38337327,  0.15964194,  0.30629508],
       [ 0.16188791,  0.55971721,  0.33561351,  0.04709838]])

>>> # Create a matrix from the transpose of A. Note the shapes 

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>>> import numpy as np

>>> # Create a simple vector.
>>> vector = np.arange(3.)
>>> vector
array([ 0.,  1.,  2.])

>>> # Create an identity with
>>> # the right dimensionality.
>>> identity = np.identity(3)

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>>> import numpy as np

>>> # Create five vectors of size two to compute the norms for.
>>> values = np.array([[v, v] for v in np.arange(0.0, 1.0, 0.2)])
>>> values
array([[ 0. ,  0. ],
       [ 0.2,  0.2],
       [ 0.4,  0.4],
       [ 0.6,  0.6],
       [ 0.8,  0.8]])

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>>> import numpy as np

>>> # Two vectors, a and b.
>>> a = np.array([-3, 4])
>>> b = np.array([4, 3])

>>> # The dot product is 0.
>>> a.dot(b)
0

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>>> import numpy as np

>>> # No scientific notation
>>> np.set_printoptions(suppress=True)

>>> # Some random orthogonal matrix.
>>> orthog = np.array([[-0.3639,  0.8268,  0.3570,  0.2377], 
                       [-0.3578, -0.5330,  0.7427,  0.1906], 
                       [-0.6208, -0.1798, -0.5609,  0.5174], 
                       [-0.5951,  0.0024, -0.0797, -0.7997]])

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