Formalization of Complex Analysis and Matrix Theory by Zhiping Shi & Yong Guan & Ximeng Li

Author:Zhiping Shi & Yong Guan & Ximeng Li
Language: eng
Format: epub
ISBN: 9789811572616
Publisher: Springer Singapore

7.1 Vector Spaces

Matrices are transforming operators in the vector space. In this section, vectors and their algebraic operations are formalized based on the FCP library in HOL4, and the linear properties of vector space are proven.

7.1.1 The Data Type for Vectors

N-dimensional vectors are elements of an N-dimension vector space, denoted by AN, where A is the element type and N is a number variable for the dimension. AN can be constructed by the N-dimensional Cartesian products of A. The function space is as follows:

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