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.