Linear Algebra: Practice Programs in Python and C Languages
Computation of Inner Products and Vector Norms by Using Python (Linear Algebra: Inner Product Spaces)
The numpy library in Python is the primary tool for computing inner products and vector norms.
Linear Algebra
PROGRAMMES
IN PYTHON AND C LANGUAGES
UNIT − III:
INNER PRODUCT SPACES
The
numpy library in Python is the primary tool for computing inner products and
vector norms.
1. Inner product (Dot product)
The
inner product of two vectors is calculated by multiplying their corresponding
elements and summing the results. For higher dimensional arrays (matrices),
numpy.inner() performs a sum product over the last axes.
Python
import numpy as np
#Define two vectors
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
# Compute the inner product
inner_product = np.inner (a,b)
print (f"inner product of a and b: (inner product}")
# For matrices, it computes the inner product of rows
x = np.array([[1, 21, [3, 4]])
y = np.array([[5, 6], [7, 8]])
inner_product_matrix = np.inner (x,y)
print (f"inner product of matrices x and y: \n
{inner_product_matrix}")
2. Vector norms
Vector
norms measure the "length" or "magnitude" of vector
numpy.linalg.norm() is used for this purpose and can compute various types of
norms based on the ord parameter.
Python
import numpy as np
v = np.array([3, 4])
#L2 Norm (Euclidean Norm) ‒ default behavior
12_norm = np.linalg.norm(v)
print (f"L2 Norm of v: {12_norm}")
#L1 Norm (Manhattan Norm)
11_norm = np.linalg.norm (v, ord‒1)
print (f"Ll Norm of v; {11_norm}")
# Max Norm (Infinity Norm)
max norm = np.linalg.norm (v,ord‒np.inf)
print (f"Max Norm of of v: {max_norm}")
# Squared L2 Norm (can be computed using inn product)
squared_12_norm = np.inner (v, v)
print (f"Squared L2 Norm of v: {squared_12_norm}")
Linear Algebra: Practice Programs in Python and C Languages : Tag: maths, mathematics : - Computation of Inner Products and Vector Norms by Using Python (Linear Algebra: Inner Product Spaces)
Linear Algebra: Practice Programs in Python and C Languages
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Linear Algebra
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