2011/10/14 by R. A. Smith, Richard A. Smith, Smith, Richard A. · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #History and Overview (math.HO) #Matrix Theory and Algorithms #Polynomial and algebraic computation #math.HO
paper · pdf · doi:10.48550/arxiv.1110.3350
Lecture notes in 10 sections for a hypothetical undergraduate course for pure math and mathematical physics students
arxiv created 2011/10/14 · openalex publication_date 2011/10/14 · arxiv updated 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space. Affine geometries are introduced and generalized by projective completion. General projective geometries are briefly introduced. Tensor products and multilinear functions are treated. The exterior algebra of a vector space and that of its dual are used in treating linear geometry and Grassmann's regressive product is treated. Scalar product spaces, orthogonality, and the Hodge star based on a general basis are covered.