References for Linear Algebra needed for Differential Equations and Linear Programming

Question

I am in need of learning the Linear Algebraic theory behind the following Applied disciplines. Could someone please recommend Linear Algebra books for:

Differential Equations: Specifically learning about characteristic values needed for solving first order linear systems with constant coefficients. As in, a proper explanation of the spaces and invariant subspaces involved when the eigenvalues are real-distinct, complex and repeated. The theory behind algebraic and geometric multiplicity of an eigenvalue and so on.

Linear Programming: Mainly focussing on Duality Theory. But would like to learn the Linear Algebra behind the Simplex Method and how a basic feasible solution is a "basis" and so on. A treatise on Convex Sets will also be useful.

I have only taken an introductory course on Linear Algebra. So I've read the first few chapters of Axler and Hoffman - Kunze. But skimming through the chapters on eigen-values, both don't seem to meet the requirements.

Any help is appreciated. Thanks in advance.

Answer 1

See my comments about Hirsch/Smale's book Differential Equations, Dynamical Systems, and Linear Algebra at the math StackExchange question Accessible topics with a background of linear Algebra and Calculus and look at Introduction to Applied Mathematics by Gilbert Strang.

Taken together (and here I mean the 1974 edition of Hirsch/Smale, not the newer edition), I think these two books have everything you're looking for in terms of content and audience and readability.

Answer 2

For the first part of your question, Volume 2 of Apostol's Calculus contains a full treatment of basic linear algebra immediately followed by chapters on differential equations.

Hoffman and Kunze covers both topics you mentioned; eigenvalues are discussed in Chapter 6 and are called "characteristic values." I think the only problem will be if you find the treatment there too theoretical.