NumPy Linear Algebra

Introduction

NumPy's linalg module provides standard linear algebra operations.

Matrix Operations

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

# Matrix multiplication
C = A @ B  # or np.dot(A, B)

# Element-wise
C = A * B

# Transpose
A.T

Linear Algebra Functions

import numpy as np

A = np.array([[1, 2], [3, 4]])

# Determinant
np.linalg.det(A)

# Inverse
np.linalg.inv(A)

# Eigenvalues and vectors
eigenvalues, eigenvectors = np.linalg.eig(A)

# Solve Ax = b
b = np.array([1, 2])
x = np.linalg.solve(A, b)

Decompositions

# SVD
U, s, Vt = np.linalg.svd(A)

# QR decomposition
Q, R = np.linalg.qr(A)

# Cholesky (for SPD matrices)
L = np.linalg.cholesky(A @ A.T + 1e-6 * np.eye(2))

Practice Problems

1. Solve system of linear equations
2. Compute matrix inverse
3. Find eigenvalues and eigenvectors
4. Perform SVD on image
5. Implement least squares regression