The famous CRC Handbook series is in the process of constructing a Handbook of Linear Algebra. Several distinguished people were asked to contribute, and Keith Geddes was asked to do the chapter on Linear Algebra in Maple. However, he has sub-contracted the job :-) to David Jeffrey and me. In this talk I will give a brief overview of the current draft of the handbook chapter. We begin with some tricks and traps of arithmetic, continue with constructors, distinguish Matrix from Array when it comes to operations, rail about row vectors, and then talk about some interesting features of LinearAlgebra in Maple that you may not be aware of; particularly the close connexion of linear algebra, eigenvalues, and polynomials. I especially want to talk about CompanionMatrix in what will be Maple 11. We end (time permitting) with some new formulae that allow fast Rayleigh Quotient iteration to find eigenvalues of certain structured matrices, which in turn give us polynomial roots (or something even more general).