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Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming ... Wiley Series of Texts, Monographs and Tracts)

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A linear combination of vectors allows any coefficient - positive or negative. A more powerful concept is the "cone" of a set of vectors which allows only positive combinations (more powerful because a linear space is the union of two cones, but a cone can never be expressed as a linear space). While there are many many good books on the "algebra of linear spaces" (i.e. Linear Algebra) I havent seen any that treat the "algebra of cones" with the thoroughness that this book does. I found this book useful to derive existence proofs in combinatorial optimization although the material is fundamental enough to be applied in many more fields. Best used if you have a reasonably good grasp of linear algebra.