Linear Algebra: Orthogonal Complements
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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.
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Hey did you know you can have 4 orthogonal lines?
It's possible. Go ahead, think about it for a bit.
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Could you do one of these problems were a basis is given and the orthogonal complement needs to be found. Thank you!
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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.
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@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.
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That is hard. Why do people invent these things? What tasks or real life problems do they help to solve?
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@dalcde I've just realised the answer. Forget about what I have asked.
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V perp, not for perpetrator, but for PERPENDICULAR!
danishfella 1 year ago 15
Thank you!
HoloUniverse 1 year ago 3