Linear Algebra 20g: The Dot Product - One of the Most Brilliant Ideas in All of Linear Algebra

[coobit]

Man, you do a great job. Keep this style of lecturing. Some guys out there need all the small details you are talking about.

[sanjursan]

The Dot Product. Don't leave home without it!

[boutiquemaths]

I've never seen anyone introduce the dot product like this. I was beaming through this whole video. So exuberant and exciting, thank you! 🤩🙏

[adarshkishore]

I love how you keep saying "Inner pro... eh, I mean dot product". It makes me more intrigued to know what the inner product is (I've never seen it in action). Excellent video!

[jfusion]

You're one of the very best, thank you for not alienating your audience not even for a second. I've been trying to understand the intuition behind the dot product for yeeeaaars, I think I'm really close now.

[cedvdb]

Thanks for agreeing that the Def of the dot product seems arbitrary the first time you see it (even though it might have enormous applications)

[evans]

My favorite interpretation is of the product P=AB is P has the same relationship to A as B has to the unit. So the dot product has the same relationship to len(w) as the projection of v (onto w as drawn) has to the unit.

[omital-ittna]

You are a frigging genius!!! I have watched hours of videos and read several articles that would help make intuitive sense of the dot product. You managed to do this in 15 minutes and now I understand it completely! Thank you!! Do you have Patreon??

[NothingMaster]

The dot (or the scalar) product is the constructed Cartesian bridge between algebra and geometry.

[mitchynz]

@4:30 Thank you! I have been stumped on the "projection of one vector to another" - that made sense with the cos theta.... but why multiply the length? Finally we get an answer

[hugopettersson]

Great video. Especially that you tell us why it’s useful

[Jacob]

You should be the guy to explain functional analysis to me :D

[JustNow]

The dot product smells a lot like Heaviside. You will find it in the equations he created that we now call Maxwells equations. Vector equations were to a large degree created by Heaviside

[MathAdam]

I'd like to see this video renamed: "The Inner pr... er, , ah... Dot Product."

[gentlemandude]

This selling of the dot product sounds like an infomerical. "The dot product... it's all you need. It has a million different uses!"

[qweify]

Thanks man, hope you are doing well :)

[swojnowski]

dot product or how much two vectors point in the same direction ;).

[OrionConstellationHome]

The Definition of the Dot Product of two vectors in Rn is UdotV=U1V1+ U2V2+...+UnVn.Then we define the norm or Length(U)of vector U in Rn using the definition of Dot we define the distance between vectors U and V in Rn as d(U, V)=IIU-VII. And only after that, in R2 and R3 we conveniently use law of Cosines for the triangle made by vectors U, V, U-V and derive the formula that you have on the board. That formula on the board is not a formal definition of the Dot Product in Linear Algebra. And the proofs of all the properties of Dot Product in Rn are also based on the formal definition and not the formula on the board. I think it is important from the beginning to buid a solid foundation by using formal definitions and not something that derived later. I like how you connect this important topic to future bigger math concepts and look forward. I really admire and appreciate your passion! Thank You!

[socialleper]

Thank you so much i was searching everywhere for an explanation like this..id calculate the scaler and think now what? is it an x? is it a y? Wheres the the bit that shows prijection onto 2nd vector..Thanks you cleared it up for me..

[engKhayre]

It's more helpful me goods times prefect