Abstract
The main objectives in this chapter are to generalize the basic geometric ideas in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\) to nontrivial higher-dimensional spaces \(\mathbb{R}^{n}\). Our approach is to start from geometric concepts in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\) and then extend them to \(\mathbb{R}^{n}\) in a purely algebraic manner.
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Notes
- 1.
This Young inequality can be easily shown by using the concavity of the logarithm function.
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Said-Houari, B. (2017). Euclidean Vector Spaces. In: Linear Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-63793-8_3
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