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Published in:
2018 | OriginalPaper | Chapter
4. GEOMETRICAL ASPECTS OF STANDARD SPACES
Author : Thomas S. Shores
Published in: Applied Linear Algebra and Matrix Analysis
Publisher: Springer International Publishing
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Abstract
The standard vector spaces have many important extra features that we have largely ignored up to this point. These extra features made it possible to do sophisticated calculations in the spaces and enhance our insight into vector spaces by appealing to geometry. For example, in the geometrical spaces \(\mathbb {R}^{2}\) and \(\mathbb {R}^{3}\) that were studied in algebra and calculus, it was possible to compute the length of a vector and angles between vectors. These are visual concepts that feel very comfortable to us. In this chapter we generalize these ideas to standard vector spaces and their subspaces. We will abstract these ideas to general vector spaces in Chapter 6.