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Inner Product Spaces - 1
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We wish to find an additional structure on a real vector space in which we can talk of the length of a vector and the angle between (non-zero) vectors. We look at R2 and R3 for inspiration. Along with the law of cosines in the trigonometry of triangle, we arrive at the notion of the dot product on R2. We look at it generalization to Rn.
Timestamp provided by Ishwarya.
00:00 Introduction
0:50 Aim of this lecture series
6:32 Discussion about the Metric Structure on a Vector space V
8:24 Length of a vector
12:07 Angle between two vectors (complex version)
23:14 Motivation for dot product
27:27 Dot product
28:37 Cauchy Schwarz Inequality
30:48 Angle between two vectors using law of cosines
36:33 End note
Timestamp provided by Ishwarya.
00:00 Introduction
0:50 Aim of this lecture series
6:32 Discussion about the Metric Structure on a Vector space V
8:24 Length of a vector
12:07 Angle between two vectors (complex version)
23:14 Motivation for dot product
27:27 Dot product
28:37 Cauchy Schwarz Inequality
30:48 Angle between two vectors using law of cosines
36:33 End note
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