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Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach

机译：线性变换，投影算子和广义逆;几何方法

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A generalized inverse of a linear transformation A: v yield w, where v and w are finite dimensional vector spaces, is defined using geometric concepts of linear transformations and projection operators. The inverse is uniquely defined in terms of specified subspaces m is a subset of v, 1 is a subset of w and a linear transformation N such that AN = O, NA = O. Such an inverse which is unique is called the 1mN-inverse. A Moore-Penrose type inverse is obtained by putting N=O. Applications to optimization problems when v and w are inner product spaces, such as least squares in a general setting, are discussed. The results given in the paper can be extended without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces. Keywords: G inverse; Linear transformation; Moore Penrose inverse; Projection operator. (jhd)

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作者
Rao, C. R.;
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年度 1988
页码 p.1-22
总页数 22
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Projective geometry; Vector spaces; Hilbert space; Least squares method; Linear systems; Linearity; Operators(Mathematics); Optimization; Sizes(Dimensions); Transformations(Mathematics); Yield;

机译：射影几何;向量空间; Hilbert空间;最小二乘法;线性系统;线性;算子（数学）;优化;尺寸（尺寸）;变换（数学）;产量;

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专利

1. A unified approach to generalized inverses of linear operators: I. Algebraic, topological and projectional properties [J] . Nashed M. Z., Votruba G. F. Bulletin of the American Mathematical Society . 1974,第5期

机译：线性算子广义逆的统一方法：I.代数，拓扑和投影性质
2. On perturbations for oblique projection generalized inverses of closed linear operators in Banach spaces [J] . Huang Q. Linear Algebra and its Applications . 2011,第12期

机译：关于Banach空间中线性闭线性算子的斜投影的广义逆。
3. Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces [J] . Wang YW, Zhang H Linear Algebra and its Applications . 2007,第1期

机译：Banach空间中封闭线性算子的斜投影广义逆的摄动分析。
4. Modification of filter responses by the generalized bilinear transformations and the inverse bilinear transformations [C] . Gargour C.S., Ramachandran V., Ramachandran R.P. Electrical and Computer Engineering, 2003. IEEE CCECE 2003. Canadian Conference on . 2003

机译：通过广义双线性变换和逆双线性变换来修改滤波器响应
5. APPLICATIONS OF GENERALIZED INVERSE TO CIRCULANT MATRICES, INTERSECTION PROJECTIONS, AND LINEAR PROGRAMMING [D] . NGUYEN, TUNG MANH 1982

机译：广义逆在循环矩阵，相交投影和线性规划中的应用
6. A linear-time algorithm that avoids inverses and computes Jackknife (leave-one-out) products like convolutions or other operators in commutative semigroups [O] . John L. Spouge, Joseph M. Ziegelbauer, Mileidy Gonzalez 2020

机译：一种线性时间算法可避免逆转和计算换乘器或其他操作员的jackknife（休留一张）产品
7. Generalized inverse of linear transformations: a geometric approach [O] . Rao C.Radhakrishna, Yanai Haruo 1985

机译：线性变换的广义逆：一种几何方法

Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach

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