ndimensional Euclidean space Multivariable Calculus Lecture 1

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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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