Linear Algebra for Computer Scientists. 5. Dot Product of Two Vectors

This computer science video is the fifth in a series about linear algebra for computer scientists. In this video you will learn how to calculate the dot product of two vectors, and why you might want to do it. You will see that the dot product of two vectors (also known as the inner product or the scalar product) results in a scalar quantity which indicates how much of the same direction two vectors have in common. You will see that the dot product can also be visualised by projecting on vector onto the other, so called orthogonal projection.
Chapters:
00:00 Dot product, inner product, scalar product
00:31 Calculate the dot product of two dimensional vectors
01:39 Calculate the dot product of three dimensional vectors
02:25 The purpose of the dot product
03:00 Add vectors together in three dimensions
03:36 The dot product of orthogonal vectors
04:36 The dot product as a measure of common direction
05:41 Orthogonal projection
08:14 A limitation of the dot product

[MM-qtdy]

I cant thank you enough, your playlists are my main source of learning you have no idea how much you helped.

god bless you

[rexrobinson]

Thank you for this video and this series.

[hoaxuan]

The variance equation for linear combinations of random variables applies to dot products (noise sensitivity.)

[abcxyz-xekz]

6:36 should it be intuitive that:
||v|| * cos(theta) ||u|| = u*v (dot product). Why does it work? I mean, is there an obvious simple answer that I am missing or the answer is not quite simple? (oh.. i guess I am asking a question in vague terms).

[bonesv]

The only thing I am questioning is that piece of like meatloaf and mashed potatoes.