number of vector components (1 Viewer)

kenkap · Apr 17, 2013

how can a vector have more than 3 components?? eg if its on a plane it will have 2, if its in space it will have 3, but how can it have 4,5,6 components?? i just dont get it..what other possible dimensions are there????? so confused

thanks

kenkap · Apr 17, 2013

D94 · Apr 17, 2013

Some dimension which the human mind cannot comprehend.

Mr Slick · Apr 18, 2013

D94 said:
Some dimension which the human mind cannot comprehend.

+1, and also, there is infinite dimensions to everything, it's a fact, yet we have only discovered 3

Mr Slick · Apr 18, 2013

https://www.youtube.com/watch?v=Q_B5GpsbSQw

Mr Slick · Apr 18, 2013

Mr Slick said:
https://www.youtube.com/watch?v=Q_B5GpsbSQw

Mind fucked :/ lol wow just wow :O

Carrotsticks · Apr 18, 2013

kenkap said:
how can a vector have more than 3 components?? eg if its on a plane it will have 2, if its in space it will have 3, but how can it have 4,5,6 components?? i just dont get it..what other possible dimensions are there????? so confused

thanks

$\\ $We can have any number of dimensions/component as we please. A component represents a dimension so for example a vector with 3 components exists in 3D space whereas a vector with 4 components exists in 4D space. Now you may be asking 'How is it possible to even have 4 dimensions?', to which the answer is the simple fact that a dimension is used to represent some variable. Many things in our world cannot simply be expressed in one or two variables/dimensions. Often, we will need several, which is the reason why we study vector spaces in N dimensions (the value of its dimension is usually defined to be the number of elements for which it's based in). We usually denote it by:$ \\\\ <v_1,v_2,v_3,...,v_n> \\\\ $Another way of expressing it (for fields) is by: $ \\\\ \mathbb{F}^n={v=(v_1,v_2,...,v_n):v_k \in \mathbb{F},k=1,2,3,...,n}$

$\\ $Actually, you have already touched on the concept of N dimensions when you studied N degree polynomials! If you define $ v_n = x^n $ you can observe linear independence (or in other words we have N dimensions) and this also touches on the concept of vector spaces of real-valued functions and their dimensions (infinite).$$

Mr Slick · Apr 18, 2013

Carrotsticks said:
$\\ $We can have any number of dimensions/component as we please. A component represents a dimension so for example a vector with 3 components exists in 3D space whereas a vector with 4 components exists in 4D space. Now you may be asking 'How is it possible to even have 4 dimensions?', to which the answer is the simple fact that a dimension is used to represent some variable. Many things in our world cannot simply be expressed in one or two variables/dimensions. Often, we will need several, which is the reason why we study vector spaces in N dimensions (the value of its dimension is usually defined to be the number of elements for which it's based in). We usually denote it by:$ \\\\ <v_1,v_2,v_3,...,v_n> \\\\ $Another way of expressing it (for fields) is by: $ \\\\ \mathbb{F}^n={v=(v_1,v_2,...,v_n):v_k \in \mathbb{F},k=1,2,3,...,n}$

$\\ $Actually, you have already touched on the concept of N dimensions when you studied N degree polynomials! If you define $ v_n = x^n $ you can observe linear independence (or in other words we have N dimensions) and this also touches on the concept of vector spaces of real-valued functions and their dimensions (infinite).$$

Fuarrrrkkk

kenkap · Apr 18, 2013

Carrotsticks said:
$\\ $We can have any number of dimensions/component as we please. A component represents a dimension so for example a vector with 3 components exists in 3D space whereas a vector with 4 components exists in 4D space. Now you may be asking 'How is it possible to even have 4 dimensions?', to which the answer is the simple fact that a dimension is used to represent some variable. Many things in our world cannot simply be expressed in one or two variables/dimensions. Often, we will need several, which is the reason why we study vector spaces in N dimensions (the value of its dimension is usually defined to be the number of elements for which it's based in). We usually denote it by:$ \\\\ <v_1,v_2,v_3,...,v_n> \\\\ $Another way of expressing it (for fields) is by: $ \\\\ \mathbb{F}^n={v=(v_1,v_2,...,v_n):v_k \in \mathbb{F},k=1,2,3,...,n}$

$\\ $Actually, you have already touched on the concept of N dimensions when you studied N degree polynomials! If you define $ v_n = x^n $ you can observe linear independence (or in other words we have N dimensions) and this also touches on the concept of vector spaces of real-valued functions and their dimensions (infinite).$$

thanks bro..your explanation has started clearing up my confusion! thanks again mate

number of vector components (1 Viewer)

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