Proposals for Matrices Tutorial

[sylee957]

• We may need some motivational examples about how eigenvals are used, than showing that it can just compute 'eigenvals'.
• Also, trying to compute determinant or inverse of fully symbolic matrix, is very rarely needed and, and it's not good to showcase how bad blows up the stuff. It may need to use practical examples how computing symbolic determinant or inverse is useful.

[sylee957]

A good example is to explore some involved matrix identities, which are almost impossible to expand by hand

I = Identity(3).as_explicit()
u = MatrixSymbol('u', 3, 1).as_explicit()
v = MatrixSymbol('v', 3, 1).as_explicit()
lhs = (I + u*v.T).inv()
rhs = I - (u*v.T) / (1 + v.dot(u))
(lhs - rhs).simplify()

[asmeurer]

The point with the symbolic inverse is specifically to show that computing certain things in closed form is bad. Maybe this should be clearer in the notebook itself.

I agree we should have more motivational examples where possible. What is a good example we can use for eigenvalues?