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Vector Definition

I have two separate definitions for vectors.

1) A vector is a list of numbers which follows the axioms of vector space.
2) A vector is any abstract object which follows the axioms of vector space.

Which definition is correct?
Neither.

A vector space is formally defined in terms of operations on a set V over a field F. Elements of V are vectors and elements of F are scalars.
Reply 2
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esrever
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Original post by SerBronn
Neither.

A vector space is formally defined in terms of operations on a set V over a field F. Elements of V are vectors and elements of F are scalars.


So vector is a list containing scalars?
Original post by esrever
So vector is a list containing scalars?

I'm not sure where you're going with this but I don't think this is a helpful way to think about vectors. Look at https://en.wikipedia.org/wiki/Vector_space

If you had, say, a 3-dimensional vector space with an orthonormal basis i, j, and k then yes, any vector can be represented by a triple (f1, f2, f3) which we understand to mean f1 i + f2 j + f3 k but that's not what it is.
Reply 4
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esrever
OP
20
Original post by SerBronn
I'm not sure where you're going with this but I don't think this is a helpful way to think about vectors. Look at https://en.wikipedia.org/wiki/Vector_space

If you had, say, a 3-dimensional vector space with an orthonormal basis i, j, and k then yes, any vector can be represented by a triple (f1, f2, f3) which we understand to mean f1 i + f2 j + f3 k but that's not what it is.


Okay thanks

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