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 | | From: | Alex Hunsley | | Subject: | formal way of describing axes: as basis vector notation? | | Date: | Sun, 23 Jan 2005 12:25:57 GMT |
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 | If working many axes when talking about geometry, it's handy to use a
more formal notation instead of x, y, z, etc.
For example, instead of writing f(x, y, z, ...), you want to write
something like:
f(e_0, e_1, .... e_n)
What would be the most obvious notation to use for this? I'm using e
above as e is used for the basis vectors for R^n but is there a better
symbol to use?
thanks
alex
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| | From: | William Elliot | | Subject: | Re: formal way of describing axes: as basis vector notation? | | Date: | Sun, 23 Jan 2005 05:40:43 -0800 |
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| On Sun, 23 Jan 2005, Alex Hunsley wrote:
> If working many axes when talking about geometry, it's handy to use a more
> formal notation instead of x, y, z, etc.
> For example, instead of writing f(x, y, z, ...), you want to write something
> like:
>
f(x1, x2,.. xj) for j-dimensional space or more common place notation
f(x_1, x_2,.. x_n) for n-space
> f(e_0, e_1, .... e_n)
> What would be the most obvious notation to use for this? I'm using e
> above as e is used for the basis vectors for R^n but is there a better
> symbol to use?
>
This is worse, in fact confusing, missing the point, going from functions
over reals to functions over vectors.
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| | From: | Alex Hunsley | | Subject: | Re: formal way of describing axes: as basis vector notation? | | Date: | Sun, 23 Jan 2005 17:50:15 GMT |
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| William Elliot wrote:
> On Sun, 23 Jan 2005, Alex Hunsley wrote:
>
>> If working many axes when talking about geometry, it's handy to use a
>> more formal notation instead of x, y, z, etc.
>> For example, instead of writing f(x, y, z, ...), you want to write
>> something like:
>>
> f(x1, x2,.. xj) for j-dimensional space or more common place notation
> f(x_1, x_2,.. x_n) for n-space
>
>> f(e_0, e_1, .... e_n)
>> What would be the most obvious notation to use for this? I'm using e
>> above as e is used for the basis vectors for R^n but is there a better
>> symbol to use?
>>
> This is worse, in fact confusing, missing the point, going from
> functions over reals to functions over vectors.
I did get the impression I was perhaps conflating vector spaces with
other things... thanks for the suggestion.
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| | From: | JEMebius | | Subject: | Re: formal way of describing axes: as basis vector notation? | | Date: | Sun, 23 Jan 2005 15:19:11 +0100 |
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| Advice: read geometry, analytic geometry and linear algebra together.
Then you will see the same things come along in different guises.
e1, e2, ... eN are commonly used in textbooks and reseach papers to
denote a set N vectors that form a basis of an N-dimensional vector
space. An arbitrary vector is commonly written as Sum (i=1...N) (x_i.e_i).
Your x, y, z would become x1, x2, x3.
There exist several variations in notations of vectors, basis vectors
and components / coordinates, but Sum (i=1...N) (x_i.e_i) is traditional.
Johan E. Mebius
Alex Hunsley wrote:
> If working many axes when talking about geometry, it's handy to use a
> more formal notation instead of x, y, z, etc.
> For example, instead of writing f(x, y, z, ...), you want to write
> something like:
>
> f(e_0, e_1, .... e_n)
>
> What would be the most obvious notation to use for this? I'm using e
> above as e is used for the basis vectors for R^n but is there a better
> symbol to use?
>
> thanks
> alex
>
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| | From: | Alex Hunsley | | Subject: | Re: formal way of describing axes: as basis vector notation? | | Date: | Sun, 23 Jan 2005 17:24:59 GMT |
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| JEMebius wrote:
> Advice: read geometry, analytic geometry and linear algebra together.
> Then you will see the same things come along in different guises.
>
> e1, e2, ... eN are commonly used in textbooks and reseach papers to
> denote a set N vectors that form a basis of an N-dimensional vector
> space. An arbitrary vector is commonly written as Sum (i=1...N) (x_i.e_i).
> Your x, y, z would become x1, x2, x3.
> There exist several variations in notations of vectors, basis vectors
> and components / coordinates, but Sum (i=1...N) (x_i.e_i) is traditional.
Thanks for clarifying this.
alex
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