5-C (SciPy)

Importing linalg module

Both A and B (import scipy.linalg and from scipy import linalg)

scipy.linalg

Module used for linear algebra

Function to find eigenvalues and eigenvectors

scipy.linalg.eig()

Function to calculate matrix rank

scipy.linalg.matrix_rank()

optimize.fsolve() input requirement

A function and initial guess

Requirements for integrate.quad()

A function, lower limit, and upper limit

Third and fourth parameters of integrate.quad()

Additional arguments for the function

Coefficient matrix format for linalg.solve()

As a NumPy 2D array

scipy.integrate.trapz()

Calculates integrals using trapezoidal rule

scipy.linalg.norm()

Calculates vector or matrix norm

scipy.optimize.root()

Finds roots of equations

scipy.linalg specialization

Linear algebra operations

scipy.linalg.pinv()

Pseudo-inverse of a matrix

scipy.linalg.lstsq()

Solves least squares problems

Reason to use SciPy

Tested, optimized, and reliable implementations

Additional information from integrate.quad()

The integral value and absolute error estimate

Second parameter of integrate.quad()

The lower limit of integration

optimize.fsolve() return on success

The solution array

Providing bounds to optimize.fsolve()

Using the bounds parameter

Function return for optimize.fsolve()

f(x) = 0 at solution