The Online Books Page

Algebras, Linear

See also what's at Wikipedia, your library, or elsewhere.

• Algebra, Universal
• Mathematical analysis
• Generalized spaces

• Line geometry
• Topology

• Algebras, Linear -- Periodicals
• Algebras, Linear -- Textbooks
• Complexes
• Nonassociative algebras
• Substitutions, Linear
• Vector spaces

• Linear algebra

• Linear Algebra (first edition; 2013), by David Cherney, Tom Denton, and Andrew Waldron, ed. by Rohit Thomas (PDF with commentary at UC Davis)
• Elementary Linear Algebra (online CC-BY edition, 2012), by Kenneth Kuttler
  • main text: PDF at saylor.org
  • solutions manual: PDF at saylor.org
• Elementary Linear Algebra (second online edition, 1998), by Keith Robert Matthews (PDF files with commentary at numbertheory.org)
• A First Course in Linear Algebra (electronic edition), by Robert A. Beezer (HTML and PDF with commentary at linear.ups.edu)
• Modern Multidimensional Calculus (Reading, MA, et al: Addison-Wesley Pub. Co., c1963), by M. Evans Munroe (page images at HathiTrust)
• Elements of Abstract and Linear Algebra, by Edwin H. Connell (PDF and Postscript at Miami)
• Elementary Divisors and Some Properties of the Lyapunov Mapping X to AX + XA* (Argonne, IL: Argonne National Laboratory, 1961), by Wallace Givens (page images at HathiTrust)

• The Electronic Journal of Linear Algebra (1996-) (full serial archives)

• Linear Algebra (third edition, 2017), by Jim Hefferon (PDF with commentary at smcvt.edu)

• Ends of Complexes (1996), by Bruce Hughes and Andrew Ranicki (PDF in the UK)
• A Treatise on the Line Complex, by C. M. Jessop (page images at Cornell)

• The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (ca. 1996), ed. by Andrew Ranicki (PDF in the UK)

• Algebraic L-Theory and Topological Manifolds (electronic edition, 2011), by Andrew Ranicki (PDF in the UK)

• The Octonions (prepublication version, 2001, with links to related materials), by John C. Baez (illustrated HTML at ucr.edu)

• Homogeneous Linear Substitutions, by Harold Hilton (page images at Cornell)
• Determinants, by Laenas Gifford Weld (page images at Cornell)
• A Short Course in the Theory of Determinants, by Laenas Gifford Weld (page images at Cornell)

• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)

• Harmonic Analysis and the Theory of Probability (Berkeley and Los Angeles: University of California Press, 1955), by S. Bochner (page images at HathiTrust)
• Mathematical Dissertations, For the Use of Students in the Modern Analysis, by J. R. Young (page images at Cornell)
• A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of The Principal Transcendental Functions (second edition; Cambridge, UK: At the University Press, 1915), by E. T. Whittaker and G. N. Watson (multiple formats at archive.org)

• A Presentation of the Theory of Hermite's Form of Lamé's Equation, by J. Brace Chittenden (page images at Cornell)

• An Elementary Treatise on Spherical Harmonics and Subjects Connected With Them, by N. M. Ferrers (page images at Cornell)

• Grassmann's Space Analysis, by E. W. Hyde (page images at Cornell)

• Operator Algebras and Quantum Statistical Mechanics, by Ola Bratteli and Derek W. Robinson
  • volume I: PDF in Norway
  • volume II: PDF in Norway

• Noncommutative Geometry, Quantum Fields and Motives (prepublication version, ca. 2008), by Alain Connes and Matilde Marcolli (PDF at alainconnes.org)
• Lectures on Graded Differential Algebras and Noncommutative Geometry, by Michel DuBois-Violette (PDF and other formats at arxiv.org)

Items below (if any) are from related and broader terms.

• A Treatise on the Line Complex, by C. M. Jessop (page images at Cornell)
• Geometrie der Dynamen: Die Zusammensetzung von Kräften und Verwandte Gegenstände der Geometrie (in German; Leipzig: B. G. Teubner, 1903), by E. Study
  • page images at HathiTrust; US access only
  • multiple formats at archive.org

• Geometric Topology: Localization, Periodicity and Galois Symmetry (The 1970 MIT Notes) (electronic edition, ca. 2005), by Dennis Sullivan, ed. by Andrew Ranicki (PDF in the UK)
• Open Problems in Topology (1990), ed. by J. van Mill and George M. Reed (PDF at Elsevier)
• Functional Analysis and Semi-Groups (New York: American Mathematical Society, 1948), by Einar Hille (multiple formats at archive.org)
• Algebraic Topology (American Mathematical Society Colloquium Publications v27; c1942), by Solomon Lefschetz (page images at HathiTrust)
• Analytic Topology (American Mathematical Society Colloquium Publications v28; 1942), by Gordon Thomas Whyburn (page images at HathiTrust)
• Topology (American Mathematical Society Colloquium Publications v12; 1930), by Solomon Lefschetz (page images at HathiTrust)

• Algebraic and Geometric Topology (proceedings of a 1983 conference at Rutgers; published 1984), ed. by Andrew Ranicki, N. Levitt, and F. Quinn (PDF and DjVu files in the UK)
• Noncommutative Localization in Algebra and Topology (electronic edition, ca. 2006), ed. by Andrew Ranicki (PDF in the UK)

• Topology (full serial archives)
• Algebraic and Geometric Topology (issues more than 5 years old free to read online) (partial serial archives)
• Geometry and Topology (issues more than 5 years old are open access) (partial serial archives)

• Topology: A Categorical Approach (Cambridge, MA: MIT Press, 2020), by Tai-Danae Bradley, Tyler Bryson, and John Terilla (PDF files with commentary at pubpub.org)

• Algebraic Topology (c2002), by Allen Hatcher (PDF files with commentary at Cornell)
• Modern Algebraic Topology (New York, Macmillan; London: Collier-Macmillan, c1963), by D. G. Bourgin (page images at HathiTrust)
• A Concise Course in Algebraic Topology (electronic edition, with errata corrected), by J. Peter May (PDF at Chicago)

• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)
• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)

• Toposes, Triples, and Theories (version 1.1, reprinted in Theory and Applications of Categories, 2005), by Michael Barr and Charles Wells (PDF in Canada)
• Category Theory for the Sciences (Cambridge, MA, and London: MIT Press, c2014), by David I. Spivak (illustrated HTML with commentary at MIT Press)
• Category Theory for Computing Science (revised reprint from Theory and Applications of Categories, 2013), by Michael Barr and Charles Wells (PDF in Canada)
• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)
• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)
• Category Theory for Programmers (free online edition), by Bartosz Milewski, ed. by Igal Tabacnik (illustrated HTML and PDF with commentary at bartoszmilewski.com and Github)

More items available under broader and related terms at left.