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This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming.
Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.
Linear Algebra and Geometry. Suetin , Alexandra I. Kostrikin , Yu I Manin. Basis and Dimension. Linear Mappings. Subspaces and Direct Sums. Quotient Spaces. The Structure of a Linear Mapping. Symplectic Space. Witts Theorem and Witts Group. Clifford Algebras. Affine and Projective Geometry. Affine Subspaces. Convex Polyhcdra and Linear Programming. Affine Quadratic Functions and Quadrics.
The Jordan Normal Form. Normed Linear Spaces. Functions of Linear Operators. Complex ification and Decomplexification. The Language of Categories. The Categorical Properties of Linear Spaces. Geometry of Spaces with an Inner Product. Classification Theorems. The Orthogonalization Algorithm and Orthogonal Polynomials. Euclidean Spaces.
Orthogonal and Unitary Operators. SelfAdjoint Operators. SelfAdjoint Operators in Quantum Mechanics. ThreeDimensional Euclidean Space. Minkowski Space. Projective Spaces. Projective Duality and Projective Quadrics. Projective Groups and Projections. The Kahler Metric. Algebraic Varieties and Hilbert Polynomials. Multilinear Algebra. The Tensor Algebra of a Linear Space. Classical Notation.
Symmetric Tensors. Tensor Products in Quantum Mechanics. Classical and Quantum Computation Alexei Yu. Kitaev , Alexander Shen , Mikhail N. Linear Algebra and Geometry P. Linear Spaces and Linear Mappings. Affine Groups. Inner Products. Unitary Spaces. Exterior Forms. Tensor Fields.
It seems that you're in Germany. We have a dedicated site for Germany. This textbook, written by a dedicated and successful pedagogue who developed the present undergraduate algebra course at Moscow State University, differs in several respects from other algebra textbooks available in English. In the first place, Kostrikin's textbook motivates many of the algebraic concepts by practical examples, for instance, the heated plate problem used to introduce linear equations in Chapter 1. In the second place, there are a large number of exercises, so that the student can convert a vague passive understanding to active mastery of the new ideas.
Introduction to Algebra