A Course of Higher Mathematics —— International Series of Monographs In: Pure and Applied Mathematics, Volume 3, Part 1

----- 《高等数学国际丛书:纯数学与应用数学》

ISBN: 9780080137179 出版年：2016 页码：337 Smirnov, V I Pergamon_RM

International Series of Monographs in Pure and Applied Mathematics, Volume 59: A Course of Higher Mathematics, III/I: Linear Algebra focuses on algebraic methods. The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus. The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups. The text is a vital source of information for students, mathematicians, and physicists.