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After becoming familiar with \(\mathbb {R}^n\) and related linear functions we now make definitions of objects which have features similar to these. In this chapter we define vector spaces and subspaces, general linear functions and the dual and matrices to represent them in a basis. Affine spaces are introduced. The (minor) changes necessary to adapt this material to the field of complex numbers are discussed.

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Vector Spaces

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  • 发表日期：

    2025年

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  • Lawrence Susanka

摘要

After becoming familiar with \(\mathbb {R}^n\) and related linear functions we now make definitions of objects which have features similar to these. In this chapter we define vector spaces and subspaces, general linear functions and the dual and matrices to represent them in a basis. Affine spaces are introduced. The (minor) changes necessary to adapt this material to the field of complex numbers are discussed.