Linear Algebra: Orthogonal Complements

[MatthewMitch23051992]

The 0 vector being in the set needs to be shown just to show the set is non-empty the first two properties hold for the empty set.

[TheBetterGamer]

Hey did you know you can have 4 orthogonal lines?

It's possible. Go ahead, think about it for a bit.

[broyalwithcheese]

Could you do one of these problems were a basis is given and the orthogonal complement needs to be found. Thank you!

[stiffz]

isn't the set of orthogonal complements also the basis?

if you dot A by any vector in its basis you get zero.

if you dot A by the null of A you get zero..

doesn't that mean that the orthogonal complement also form a basis, and the basis form an orthogonal complements? I'm going crazy trying to figure out the difference.

[comecra85]

That is hard. Why do people invent these things? What tasks or real life problems do they help to solve?

[AA10Megaviv]

@comecra85 In fact, as much as I know (weird terminology...) "these things", meaning the whole formalization and exploration of the algebra of the 1 and 2 dimensional mathematical objects: vectors & matrices consisting Linear Algebra, are the building blocks for "other things" investigated by natural sciences, which doubtlessly help to solve a wide variety of real life problems (consider the microwave). Anyway, whether you believe it or not, some people (like me) actually enjoy these inquiries.

[danishfella]

V perp, not for perpetrator, but for PERPENDICULAR!

[dalcde]

Is it true that there are infinite number of orthogonal components of a subspace V?

[dalcde]

@dalcde I've just realised the answer. Forget about what I have asked.

[HoloUniverse]

Thank you!

[grimmovers]

thnx

[mahlejas]

it is not so important but at 10:26 Rn sould be that Rm.

FYI.

Thanks for your videos they are so helpful.

[yynotx]

r transpose vectors are confusing

[Soymilllk]

i dont like the new writing style! i miss the cool old pixelated numbers and diagrams!