Linear algebra is a fundamental task for mathematical software. Linear algebra is easily automated because it involves tedious computations that must be performed according to well-defined formulas and algorithms. Sage has extensive support for various types of calculations with vectors and matrices. Sage's vector and matrix objects build upon the basic mathematical types that we learned about in Chapter 3. We will also learn about a Python library called NumPy that is very useful for numerical calculations.
In this chapter we will:
Learn how to create and manipulate vector and matrix objects
See how Sage can take the tedious work out of linear algebra
Learn about matrix methods for computing eigenvalues, inverses, and decompositions
Get started with NumPy arrays and matrices for numerical calculations
There are many ways to do linear algebra in Sage. Sage is a collection of tools, each of which has its own way of representing vectors and matrices...