Orthogonal complement of the orthogonal complement | Linear Algebra | Khan Academy

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Finding that the orthogonal complement of the orthogonal complement of V is V
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[@alexandertmackay]

Great proof. But to be more specific, the orthogonal compliment of the orthogonal compliment of V is the closure of V. This proof is assuming that V is already closed. It can be easily shown in the first stages that the orthogonal compliment of V is equivelent to the orthogonal compliment of the closure of V. The rest follows as you have shown.

[@Dominoes0]

The videos in this section could really benefit from numerical and graphical examples, like in the earlier ones. They're much harder to grasp as a result.

[@stekim]

Thanks again khan, saving me one video at a time

[@saiouln.8060]

Awesome as always!

[@desrucca]

I genuinely dont understand why would someone questioning how to proof that For me its obvious that Orthogonality means Independence (perpendicularity) between two vectors including all of the linear combinations. Therefore its impossible for orthogonal complements to be outside of the orthogonal of its original subspace Its like trying to find other number than zero itself that always multiplies any given number to zero.

[@noorulhuda2195]

is this true only for the space Rn ? or any space?

[@DuderofDudeness]

perp perp perp

[@c.y.6703]

perpendicular?

[@michaelperes2257]

He blabs for hours. He made like 10 vids on this topic but cant make one example. WHAT A WASTE OF TIME!