Linear Algebra and Geometry
Linear Algebra and Geometry
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DOI：
10.2307/3618166
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发表时间：
1989-07
期刊：
影响因子：
--
通讯作者：
P. K. Suetin;A. Kostrikin;Y. Manin
中科院分区：
文献类型：
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作者：
P. K. Suetin;A. Kostrikin;Y. Manin
第 1 部分 线性空间和线性映射：线性空间基础和维度 线性映射 矩阵子空间和直和商空间 对偶 线性映射的结构 Jordan 范式规范线性空间 线性算子的函数 复杂化和解复杂化 类别语言 线性空间的分类属性。第二部分 具有内积的空间几何：关于几何内积分类定理、正交化算法和正交多项式、欧几里得空间、酉空间、正交和酉算子、自伴算子、量子力学中的自伴算子、二次形式的几何和自伴算子的特征值、三维欧几里得空间、明可夫斯基空间、辛空间、维特定理和维特群克利福德代数。第三部分 仿射和射影几何：仿射空间、仿射映射和仿射坐标 仿射群 仿射子空间 凸多面体和线性规划 仿射二次函数和二次函数 射影对偶性和射影二次曲线 射影群和投影 笛沙格和帕普斯的配置和经典射影几何 卡勒度量代数簇和希尔伯特多项式。第四部分 多重线性代数：线性空间的张量积 正则同构和张量积的线性映射 线性空间的张量代数 经典表示法 对称张量 斜对称张量 以及线性空间外部的外代数 形成量子力学中的张量场张量积。
Part 1 Linear spaces and linear mappings: linear spaces basis and dimension linear mappings matrices subspaces and direct sums quotient spaces duality the structure of a linear mapping the Jordan normal form normed linear spaces functions of linear operators complexification and decomplexification the language of categories the categorical properties of linear spaces. Part 2 Geometry of spaces with an inner product: on geometry inner products classification theorems the orthogonalization algorithm and orthogonal polynomials Euclidian spaces unitary spaces orthogonal and unitary operators self-adjoint operators self-adjoint operators in quantum mechanics the geometry of quadratic forms and the Eigenvalues of self-adjoint operators three-dimensional Euclidean space Minkowski space symplectic space Witt's theorem and Witt's group Clifford algebras. Part 3 Affine and projective geometry: affine spaces, affine mappings and affine coordinates affine groups affine subspaces convex polyhedra and linear programming affine quadratic functions and quadrics projective duality and projective quadrics projective groups and projections Desargues' and Pappus' configurations and classical projective geometry the Kahler metric algebraic varieties and Hilbert polynomials. Part 4 Multilinear algebra: tensor products of linear spaces canonical isomorphisms and linear mappings of tensor products the tensor algebra of a linear space classical notation symmetric tensors skew-symmetric tensors and the exterior algebra of a linear space exterior forms tensor fields tensor products in quantum mechanics.