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- Thread starter Mr Davis 97
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jedishrfu

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While its true that you can represent the vector in component form using any real number that component value isn't the vector itself ie for the real value of 5 and the one dimensional vector <5>

5 =/= <5>

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Okay, that makes sense. But, for example, what if I were trying to define a function that mapped one-dimensional vectors to one-dimensional vectors. What notation could I use to specify this without the reader getting confused with whether I mean real numbers? ##f: \mathbb{R} \to \mathbb{R}## seems to be ambiguous...

While its true that you can represent the vector in component form using any real number that component value isn't the vector itself ie for the real value of 5 and the one dimensional vector <5>

5 =/= <5>

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jedishrfu

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Other examples are described here

https://en.m.wikipedia.org/wiki/Vector_notation

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mathman

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Is this why in 1D kinematics we solve problems as if the equations were a scalar equations rather than a vector ones, when we really mean vectors? They are in one-to-one correspondence, so are we just being lazy by not wring something like ##\vec{v_0} = v_0\hat{j}##?

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lavinia

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A field can always be considered to be a one dimensional vector space over itself. The field is both the field of scalars for this vector space and it is the vector space itself.

So the real numbers are a one dimensional vector space over itself and the complex numbers are a one dimensional vector space over itself. In the first case, the field of scalars is the real numbers, in the second, the field of complex numbers.

So the real numbers are a one dimensional vector space over itself and the complex numbers are a one dimensional vector space over itself. In the first case, the field of scalars is the real numbers, in the second, the field of complex numbers.

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Ssnow

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mathwonk

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