SciPy linalg basics

scipy.linalg extends NumPy linear algebra with decompositions (LU, QR, Cholesky), matrix functions, and numerically stable solvers for dense problems.

When scipy.linalg vs np.linalg

• Small solves: either np.linalg.solve or linalg.solve
• Decompositions: linalg.lu, linalg.qr, linalg.cholesky
• Matrix exponentials, norms, determinants with LAPACK backends

Array dtypes

Use float64 for stability unless memory forces float32. Ill-conditioned matrices need condition number checks via linalg.cond.

Norm and det

import numpy as np
from scipy import linalg

A = np.array([[1., 2.], [3., 4.]])
print('det:', linalg.det(A))
print('norm:', linalg.norm(A))
print('cond:', linalg.cond(A))

Important interview questions and answers

1. Q: Condition number?
   A: Ratio relating input perturbation to output error—large cond means unstable solve.
2. Q: Why float64?
   A: Single precision can fail subtle LA tasks; production numerics often default to double.

Self-check

1. Name three scipy.linalg capabilities beyond np.linalg.solve.
2. What does a large condition number warn you about?

Tip: Check linalg.cond(A) before trusting solves on nearly singular matrices.