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This PPT explains how the np linalg norm function in NumPy helps compute vector and matrix magnitudes efficiently. Learn different types of norms, their real-world applications in data science and machine learning, and how to use np linalg norm for numerical and linear algebra computations in Python.
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Understanding np.linalg.norm in Python A comprehensive guide to computing vector and matrix norms using NumPy's powerful linear algebra toolkit
What is np.linalg.norm? Core Function Key Applications np linalg norm is NumPy's built-in function for calculating various types of norms (magnitude or length) of vectors, matrices, and higher-dimensional arrays. • Computing vector magnitudes and distances • Normalizing data for ML models • Measuring matrix properties • Optimization convergence checks Essential for data science, machine learning distance calculations, optimization algorithms, and numerical analysis workflows.
Common Norm Types & Syntax L1 Norm (Manhattan) L2 Norm (Euclidean) Infinity Norm np.linalg.norm(x, ord=1) np.linalg.norm(x, ord=2) np.linalg.norm(x, ord=np.inf) Sum of absolute values. Useful for sparse data and feature selection. Square root of sum of squares. Default norm, measures straight-line distance. Maximum absolute value. Useful for worst-case scenarios and error bounds.
Practical Code Examples Basic Vector Norm Matrix Norms import numpy as np# Create a vectorvector = np.array([3, 4])# Calculate L2 norm (default)magnitude = np.linalg.norm(vector)print(magnitude) # Output: 5.0# Calculate L1 norml1_norm = np.linalg.norm(vector, ord=1)print(l1_norm) # Output: 7.0 import numpy as np# Create a matrixmatrix = np.array([[1, 2], [3, 4]])# Frobenius normfrob = np.linalg.norm(matrix)print(frob) # 5.477# Max column sumcol_norm = np.linalg.norm( matrix, ord=1)print(col_norm) # 6.0 These examples demonstrate real-world applications: computing vector distances, normalizing features, and analyzing matrix properties in data processing pipelines.
Advanced Parameters & Options 01 02 03 axis Parameter keepdims Parameter ord Parameter Options Specify which axis to compute norms along. Use axis=0 for column-wise, axis=1 for row-wise, or None (default) for entire array. Set keepdims=True to retain reduced dimensions as size 1, preserving array structure for broadcasting operations. Choose from None, 1, 2, -1, -2, np.inf, -np.inf for vectors, or 'fro', 'nuc', 1, 2, -1, -2, np.inf, -np.inf for matrices.
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