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Vectors - write ordered triples in vertical or horizontal form?
- Thread starter Outrageous
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In summary, the conversation discusses the difference between writing vectors in horizontal or vertical form, with the conclusion that it is more convenient to write them horizontally. The topic of dual spaces and matrix multiplication is also briefly mentioned as a more abstract and advanced concept.
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tiny-tim
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Hi Outrageous! 
(i'm puzzled as to why you said "complex" … you're not thinking of quaternions, are you?)
horizontal or vertical are both vectors
one is covariant, the other is contravariant (i can never remember which is which
)
(i'm puzzled as to why you said "complex" … you're not thinking of quaternions, are you?
)Outrageous said:
horizontal or vertical are both vectors
one is covariant, the other is contravariant (i can never remember which is which
)for most purposes, it doesn't matter, so you might as well write everything horizontally, since that's more convenient! 
- #3
Outrageous
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Thank you. That should be vector.
How to edit title?
How to edit title?
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tiny-tim
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i don't think can edit the title
(but you can edit the first post, to say "ignore the title!")
(but you can edit the first post, to say "ignore the title!"
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Mark44
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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.
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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Outrageous
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Really advanced. Thank you.
1. What is a vector?
A vector is a mathematical object that represents both magnitude and direction. It is typically represented as an ordered triple or a column/row of numbers.
2. How do you write a vector in ordered triple form?
In ordered triple form, a vector is written as (x, y, z) where x, y, and z represent the components of the vector in the x, y, and z directions respectively.
3. Can a vector be written in both vertical and horizontal form?
Yes, a vector can be written in both vertical and horizontal form. In vertical form, a vector is written as a column vector with the components stacked on top of each other. In horizontal form, a vector is written as a row vector with the components written side by side.
4. How do you convert a vector from horizontal to vertical form?
To convert a vector from horizontal to vertical form, simply write the components of the vector one on top of the other, creating a column vector.
5. How do vectors help in scientific research?
Vectors are useful in scientific research as they allow for the representation and analysis of physical quantities with both magnitude and direction, such as force, velocity, and acceleration. They are also used in mathematical models and simulations to describe and predict the behavior of complex systems.
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