TY - BOOK ID - 4788661 TI - Linear Algebra and Geometry AU - Shafarevich, Igor R. AU - Remizov, Alexey O. PY - 2013 SN - 9783642309946 9783642309939 3642309933 3642309941 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Linear and Multilinear Algebras, Matrix Theory. KW - Algebra. KW - Geometry. KW - Associative Rings and Algebras. KW - Matrix theory. KW - Mathématiques KW - Algèbre KW - Géométrie KW - Algebras, Linear. KW - Algebras. KW - Algebras, Linear KW - Geometry KW - Mathematics KW - Physical Sciences & Mathematics KW - Algebra KW - Linear algebra KW - Associative rings. KW - Rings (Algebra). KW - Euclid's Elements KW - Algebra, Universal KW - Generalized spaces KW - Mathematical analysis KW - Calculus of operations KW - Line geometry KW - Topology KW - Rings (Algebra) KW - Algebraic rings KW - Ring theory KW - Algebraic fields UR - https://www.unicat.be/uniCat?func=search&query=sysid:4788661 AB - This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics. ER -