Linear Algebra with Scipy

Google some scipy tutorials. They'll be better. This worksheet is just more specialize for our 308 class

http://docs.sympy.org/0.7.5/index.html

What is Scipy?

A Python stack consisting of libraries that are particularly used for STEM. We'll likely use a lot of sympy here because we're interested in symbolic calculations. But you should also know of scipy and numpy for numerical calculations.

See http://live.sympy.org/ for a live shell.

In [13]:

from sympy import *
x, y, z, t = symbols('x y z t')
import numpy as np

Echelon Forms

This is not even implemented in scipy or numpy. See https://stackoverflow.com/questions/7664246/python-built-in-function-to-do-matrix-reduction for a discussion.

Problem 1 http://kevinlui.org/m308exams/au17_midterm1sol.pdf

In [4]:

A = Matrix([
           [1, 2, -1, 3],
           [0, 1, -1, 2],
           [0, 0, 1, 1]
           ])

In [6]:

A.rref()

(Matrix([
 [1, 0, 0, -2],
 [0, 1, 0,  3],
 [0, 0, 1,  1]]), (0, 1, 2))

Solving Linear System

Problem 1 http://kevinlui.org/m308exams/au17_midterm1sol.pdf

In [16]:

A = Matrix([
           [1, 2, -1, 3],
           [0, 1, -1, 2],
           [0, 0, 1, 1]
           ])

In [17]:

b = Matrix([
        [1],
        [1],
        [0]
        ])

In [18]:

linsolve((A, b), [t, x, y, z])

{(2*z - 1, -3*z + 1, -z, z)}