This is a two-volume course in Linear Algebra. We treat topics that are important to the Physicist or Engineer that get scant treatment in most Linear Algebra books. We begin with some elementary Group Theory. While that presents a difficult beginning, it makes possible a simpler and better treatment of subsequent topics. Throughout, the treatment is unusually geometric, as that intuition is part of the beauty of the subject, and is very important for the Physicist or Engineer to cultivate.
Volume 1 begins with an unusually thorough treatment of basic Linear Algebra, followed by a treatment of rotations, and Hermitian matrices with unusual care, and some background to Numerical Analysis. Volume 2 treats some topics that are just around the corner from Linear Algebra. We treat Linear Algebra applied to ODE and PDE, then Tensors, Functional Analysis, Integral Equations, Lie Groups, Lattices, Elliptic Function Theory, Euler Angles, the Coriolis Force, and a deeper look at Conic Sections
This book could be considered a companion to my book on Classical Mechanics, but stands on its own quite well.
Mathematicians will also find this treatment a very good treatment of Linear Algebra in most of the fundamental issues, and will show applications not usually seen by mathematicians.