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Inner Product Spaces - 5 (Orthogonal Vectors and Orthogonal Projection)
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We define the notion of orthogonal vectors. By a geometric argument, we arrive at the notion of the orthogonal projection of a vector v on to the 1-dimensional subspace spanned by a nonzero vector u.
Timestamp provided by Ishwarya.
00:00 Introduction
0:50 Motive of this lecture
3:52 Recap of previous concepts
5:30 When do we say two vectors are perpendicular to each other?
6:55 Definition - Orthogonal vectors
9:58 Example
13:39 Orthogonal projection (Geometric approach)
14:42 Orthogonal projection of v onto Ru , u a unit vector)
18:47 Example
20:54 Summary
30:00 Orthogonal projection of v along any nonzero vector u (u not necessarily unit vector)
32:47 Formula
37:37 Any vector in R2 can be expressed as sum of two Orthogonal vectors
41:50 Trade secret
42:48 Endnote of the lecture
Timestamp provided by Ishwarya.
00:00 Introduction
0:50 Motive of this lecture
3:52 Recap of previous concepts
5:30 When do we say two vectors are perpendicular to each other?
6:55 Definition - Orthogonal vectors
9:58 Example
13:39 Orthogonal projection (Geometric approach)
14:42 Orthogonal projection of v onto Ru , u a unit vector)
18:47 Example
20:54 Summary
30:00 Orthogonal projection of v along any nonzero vector u (u not necessarily unit vector)
32:47 Formula
37:37 Any vector in R2 can be expressed as sum of two Orthogonal vectors
41:50 Trade secret
42:48 Endnote of the lecture
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