Math Help - Vectors definiton

Hi, everyone, it's been a while!

I have a question about vectors.

Searching on internet for definition of vectors I often get that vectors are quantities with ability to represent magnitude and direction simultaneously.

In my math book there isn't definition of vectors, just explanation, but as I understand it, vectors are objects similar to sets or arrays, they can hold more elements then scalar quantities which are generaly numbers. So vectors can hold two or more numbers, lines, shapes or any math objects which are in specific relation.

Is my interpretation of vectors correct and can someone give me exact math definiton of vectors?

Originally Posted by OReilly

Hi, everyone, it's been a while!

I have a question about vectors.

Searching on internet for definition of vectors I often get that vectors are quantities with ability to represent magnitude and direction simultaneously.

In my math book there isn't definition of vectors, just explanation, but as I understand it, vectors are objects similar to sets or arrays, they can hold more elements then scalar quantities which are generaly numbers. So vectors can hold two or more numbers, lines, shapes or any math objects which are in specific relation.

Is my interpretation of vectors correct and can someone give me exact math definiton of vectors?

Scalars and vectors are examples of a class of objects known as tensors (specifically "tensor fields," to be Mathematically precise.) Scalars are 0 rank tensors and vectors are 1st rank tensors, if I have the terminology right. Check here for a good starting point.

-Dan

I think of scalars as element of a field.
And vectors are elements in a vector space over the field.
But that is not what you were asking?

First, a disclaimer: I am trained in real analysis, topology, and foundation of mathematics (philosophy of mathematics). That of course means that I think that any mathematical object is a set.

When I taught vector analysis, I would always begin by saying “vectors are objects that have both direction and length”. “Thus as such a vector is not a strictly a mathematical object".

Originally Posted by Plato

When I taught vector analysis, I would always begin by saying “vectors are objects that have both direction and length”.

I am sure you know there is a mathematical version of vector analysis. But students in your vector analysis class (engineers) do not care about such things.

Originally Posted by ThePerfectHacker

I am sure you know there is a mathematical version of vector analysis. But students in your vector analysis class (engineers) do not care about such things.

That happens to be exactly my point. Mathematics is not a science.
Engineers can choose to apply a model as they choose.
That is, they cannot blame mathematician for their mistakes.

Originally Posted by OReilly

Hi, everyone, it's been a while!

I have a question about vectors.

Searching on internet for definition of vectors I often get that vectors are quantities with ability to represent magnitude and direction simultaneously.

In my math book there isn't definition of vectors, just explanation, but as I understand it, vectors are objects similar to sets or arrays, they can hold more elements then scalar quantities which are generaly numbers. So vectors can hold two or more numbers, lines, shapes or any math objects which are in specific relation.

Is my interpretation of vectors correct and can someone give me exact math definiton of vectors?

To be pedantic in mathematics a vector is an element of a Vector Space.

RonL