SciPy — Linear Algebra

Solve linear system

from scipy import linalg
import numpy as np

A = np.array([[3, 1], [1, 2]])
b = np.array([9, 8])

x = linalg.solve(A, b)
print(f"Solution: {x}")

Matrix operations

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

# Matrix multiplication
C = A @ B
print(f"A * B =\n{C}")

# Inverse
A_inv = linalg.inv(A)
print(f"Inverse of A =\n{A_inv}")

# Determinant
det = linalg.det(A)
print(f"Determinant = {det:.2f}")

Eigenvalues and eigenvectors

A = np.array([[4, 2], [1, 3]])
eigenvalues, eigenvectors = linalg.eig(A)
print(f"Eigenvalues: {eigenvalues}")
print(f"Eigenvectors:\n{eigenvectors}")

Singular Value Decomposition

A = np.array([[1, 2], [3, 4], [5, 6]])
U, s, Vh = linalg.svd(A)
print(f"U shape: {U.shape}")
print(f"Singular values: {s}")
print(f"Vh shape: {Vh.shape}")

LU decomposition

A = np.array([[1, 2], [3, 4]])
P, L, U = linalg.lu(A)
print(f"Permutation:\n{P}")
print(f"Lower:\n{L}")
print(f"Upper:\n{U}")

Cholesky decomposition

A = np.array([[4, 2], [2, 3]])
L = linalg.cholesky(A)
print(f"Cholesky factor:\n{L}")

Matrix norm

A = np.array([[1, 2], [3, 4]])
norm = linalg.norm(A)
print(f"Frobenius norm: {norm:.4f}")

Mini Practice

1. Solve a linear system
2. Compute eigenvalues
3. Perform SVD
4. Decompose a matrix

Up Next

Continue with FFT - Fast Fourier Transform.