Orthogonal Complements | How to Find a Basis for "W Perp" [Passing Linear Algebra]

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[@christopherandrewmartin494]

This was a super helpful video for me as I am studying for my linear algebra midterm. Thank you so much!!!

[@christopherandrewmartin494]

Also I loved the pun at the beginning lol

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[@harrisoncaldwell4541]

You are helping me pass linear algebra.

[@waqaskhalique1485]

finally got the concept.. thanks

[@B3SSPR0]

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[@1forge2rulethemall88]

life saver for linear algebra

[@DanielOlma]

at 6:33 you don't explain how you get to those numbers that follow. You seemed to skip a step.

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[@hubbadubchub]

Many thanks for the explanation!

[@indrashispowali]

compliment is different from complement

[@vincentkinduelo9586]

GREAT CATCH INDRASHIS

[@iced751]

At 6:44 shouldn't it be -z since our x component = 3y - z or is it always a + sign

[@Laucher-]

Thank you so much for these!

[@halogen4460]

You said that W perp is perpendicular to the original 1/2*x line, but there are infinite lines that are perpendicular. Is W perp the one you chose because it goes through the origin because vector spaces and subspaces must contain the 0 vector?

[@cadenorris4009]

If you have W perp not going through the origin, it turns out that they are NOT perpendicular necessarily to every vector in W

[@axelfarber1569]

Your eyes are so pretty.

[@erminioottone3738]

wait a minute, at 5:24 you said that dim of w is 2 and dim of w^orth is equal to 1, hence dimw + dimw^orth=3 which is different from dimW=2

[@孫傅康]

Thank you sooo much!

[@davidchang3088]

thank you sir

[@yvfk]

Great video!

[@KlavaKoshka]

Thanks so much for this!

[@raymondblake5765]

If You have the vector (a, b, c) then it is orthogonal to all of the vectors on the plane in R^3 defined by ax + by +cz= 0, because (a, b, c) •(x, y, z) = 0. Also if you have the plane in r^3 given by ax +by +cz =0, then the vector (a, b, c) is orthogonal to all the vectors on this plane. Did you show this method to find the orthogonal compliment because it is generalizable to higher dimensions?

[@rahulgosavi492]

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Good

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W video indeed

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“Double You Perp” -Cool kid

[@wormius51]

This video is very orthogonal. I'll give you that.

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Had to subscribe after your joke XD

[@terellkantwell6876]

why did you transpose the basis at 8:50 ???

[@stemsupport3645]

I was using a theorem that I derive in this video: kzbin.info/www/bejne/r57chXmnoqaoaJY Hope this helps!

[@vivoroses6267]

THANK U MAN

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[@hairold5680]

What the fuck

[@zhou6075]

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[@MikkelNicolaysen-g5h]

dont you have to normalize in the end?

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[@jroseme]

Counting down the days to flush this knowledge forever. Thanks for the help until then.

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[@Diaming787]

Video starts at 00:30

[@kapjoteh]

It starts at 0:00 you silly goose

[@DanielOlma]

And how does y = y and z = z. There is no logical transition. It might seem obvious, but there are skipped steps. Pretend you are creating a video that explains this to a child.

[@sihaskumarasingha8148]

Actually, (W⊥)⊥ ⊇ W, not equal to W, right?