Dot Product of Two Vectors, n-Space - Linear Algebra

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Science Education linear algebra elementary linear algebra vector space linear algebra dot product linear algebra vector space proof linear algebra vector spaces vector spaces linear algebra linear algebra vector space properties linear algebra vector space examples

This video explains the dot product of two vectors, including the formula, symbol, how to calculate it dot product of the IJ vectors and why is ij zero.

0:00 Dot product, geometric interpretation
3:15 Component form of the dot product
7:31 Dot product in n-space
9:01 Properties of the dot product
12:40 Cauchy-Schwarz inequality, defining the angle in n-space
14:45 Triangle inequality for vectors and distance
16:46 Evaluating the dot product using matrix multiplication

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