n-dimensional Euclidean space (Multivariable Calculus Lecture #1)
Автор: Scott Armstrong
Загружено: 2021-01-31
Просмотров: 2151
Описание:
We introduce n-dimensional Euclidean space and the basic vector space binary operations. We explain how the geometry of R^n is encoded by its natural inner (or dot) product, and we state and prove the Cauchy-Schwarz inequality.
Contents
0:00 - Overview
2:22 - Vector space structure of R^n
8:06 - The equation of a line in parametric form
15:25 - Inner product space structure of R^n
17:04 - Euclidean distance
18:28 - Angle between two vectors
23:39 - The Cauchy-Schwarz and triangle inequalities
29:45 - Examples
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