 | Introduction to Linear Algebra, Third Edition by Gilbert Strang
Buy used from: $46.53 A great introduction. Also see Prof. Strang's wonderful video lectures at MIT OCW.
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 | Linear Algebra by Georgi E. Shilov
Buy new: $11.53 / Used from: $7.95 A beautiful linear algebra book.
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 | Matrix Analysis by Roger A. Horn
Buy new: $37.80 / Used from: $33.61 Classic introduction to Matrix Analysis.
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 | Topics in Matrix Analysis by Roger A. Horn
Buy new: $56.26 / Used from: $50.40 Followup.
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 | Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition) by Gene H. Golub
Buy new: $40.84 / Used from: $22.50 Best text on numerical linear algebra. Computer Science for linear algebraist.
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 | Direct Methods for Sparse Matrices (Numerical Mathematics and Scientific Computation) by I. S. Duff
Buy new: $74.00 / Used from: $58.00 Technology for sparse matrices. More Computer Science for linear algebraist.
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 | Advanced Linear Algebra (Graduate Texts in Mathematics) by Steven Roman
Buy used from: $10.91 Round off loose ends.
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 | Finite-Dimensional Vector Spaces by P.R. Halmos
Buy new: $53.95 / Used from: $29.55 Vector spaces.
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 | Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi
Buy new: $147.23 / Used from: $82.97 Let the payoff begin. Matrices in graph theory.
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 | Combinatorial Matrix Classes (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi
Buy new: $122.55 / Used from: $66.50 Follow-up to Brualdi's classic text. Much more in-depth and mostly independent from its predecessor.
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 | Extremal Combinatorics: With Applications in Computer Science by Stasys Jukna
Buy new: $71.96 / Used from: $66.96 Excellent discussion of the "Linear Algebra Method" in combinatorics among other things. The best reference for the Linear Algebra Method remains the monograph by Babai and Frankl.
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 | Matrices in Combinatorics and Graph Theory (Network Theory and Applications Volume 3) by Bolian Liu
Buy new: $118.55 / Used from: $120.29 More matrices in graph theory.
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 | Matroid Theory (Oxford Graduate Texts in Mathematics) by James G. Oxley
Buy new: $56.45 / Used from: $40.00 Most accessible and thorough introduction to the matroids.
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 | Greedoids (Algorithms and Combinatorics) by B. H. Korte
Buy used from: $154.11 Many extentions of matroids.
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 | Optimization by Vector Space Methods (Series in Decision and Control) by David G. Luenberger
Buy new: $102.91 / Used from: $84.76 The way to optimization.
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 | Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6) by Dimitris Bertsimas
Buy new: $89.00 / Used from: $64.00 The best book on LP
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 | Random Matrices, Volume 142, Third Edition (Pure and Applied Mathematics) by Madan Lal Mehta
Buy new: $87.75 / Used from: $60.00 See random projection method book later for a flavor of applications of Random matrices.
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 | The Random Projection Method (Dimacs Series in Discrete Math) by Santosh S. Vempala
Buy new: $41.00 / Used from: $69.88 The classic introduction to randomized projection method. RPs are one of the ways to escape the 'curse of dimensionality'. Deep, yet reasonably accessible.
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