We have seen that Sage can reduce or eliminate the tedious computations that are required when doing linear algebra by hand. The capabilities of Sage are equivalent to those found in commercial mathematical software systems. Specifically, we covered:
Creating vector spaces and vector objects, and performing basic operations like inner products and cross products
Creating matrix objects, performing elementary row operations, and matrix algebra
Using matrix methods to calculate scalars and matrices such as determinants, inverses, eigenvalues, and eigenvectors
Using matrix methods to factorize and decompose matrices
Creating and manipulating NumPy arrays and matrices for working with numerical data
In the next chapter, we will learn about the plotting and graphics capabilities of Sage.