Vectors - write ordered triples in vertical or horizontal form?

  • Thread starter Outrageous
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  • #1
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A= i +j+k
A=(1,1,1)
can I write in vertical as shown?
is there any difference between them?

Thank you
 

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  • #2
tiny-tim
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Hi Outrageous! :smile:

(i'm puzzled as to why you said "complex" … you're not thinking of quaternions, are you? :confused:)
A= i +j+k
A=(1,1,1)
can I write in vertical as shown?
is there any difference between them?
horizontal or vertical are both vectors

one is covariant, the other is contravariant (i can never remember which is which :redface:)

for most purposes, it doesn't matter, so you might as well write everything horizontally, since that's more convenient! o:)
 
  • #3
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Thank you. That should be vector.
How to edit title?
 
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  • #4
tiny-tim
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i don't think can edit the title :smile:

(but you can edit the first post, to say "ignore the title!!" o:))
 
  • #6
HallsofIvy
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This is a bit more abstract and advanced but one way of looking at it is this: Given an n-dimensional vector space, V, over field F, the set of all functions from V to F, the "dual space" to V, is itself a vector space, V*, with addition defined by (f+ g)(v)= f(v)+ g(v) and (af)v= a(f(v)), also of dimenion n. We can then represent functions in V* as "row matrices" and the vectors in V as "column matrices" so that the operation f(v) is a matrix multipication.

However, because it is still true that V and V*, both being n-dimensional vector spaces, are isomorphic we can identify one with the other, the row and column matrices as both representing vectors and think of the matrix multiplication as an "inner product" on a vector space.
 
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  • #7
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Really advanced. Thank you.
 

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