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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.

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  • $\begingroup$ @Amzoti: No. I'll see if I can find them. Thanks. $\endgroup$ – Ishfaaq Oct 1 '14 at 8:43
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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.

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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.

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  • $\begingroup$ The style in Hoffman & Kunze is fine. I'm just not sure the emphasis is on what I need. Specifically I need to know what's happening when eigenvalues for a matrix are real-distinct, complex or repeated. And what are the concepts behind multiplicity in repeated eigenvalues. $\endgroup$ – Ishfaaq Oct 1 '14 at 2:38
  • $\begingroup$ That is certainly addressed. That's a big part of what the chapters on "elementary canonical forms" and "rational and Jordan forms" are about. $\endgroup$ – user180040 Oct 1 '14 at 2:47

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