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shaharhada1
 Post subject: question
PostPosted: Fri, 1 Jul 2011 02:34:52 UTC 
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What the difference between scalar to vector?
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outermeasure
 Post subject: Re: question
PostPosted: Fri, 1 Jul 2011 15:53:43 UTC 
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shaharhada1 wrote:
What the difference between scalar to vector?


what vector?

For any field K, K is a perfectly good K-vectorspace. On the other hand, a K-vectorspace V need not carry a field structure (it might not even be a ring).

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: question
PostPosted: Fri, 1 Jul 2011 22:11:40 UTC 
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shaharhada1 wrote:
What the difference between scalar to vector?


You should provide some context for this.

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shaharhada1
 Post subject: I have a question
PostPosted: Fri, 1 Jul 2011 23:37:32 UTC 
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Is k a vector?
if it is, what the difference between it to scalar that called M?
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Soroban
 Post subject: Re: question
PostPosted: Sat, 2 Jul 2011 23:12:13 UTC 
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Hello, shaharhada1!

Quote:
What is the difference between a scalar and a vector?

A scalar is a numerical quantity. .It has magnitude (size) only.

Examples: A car is moving at 55 miles per hour.
. . . . . . . . A ball is thrown at 30 feet per second.


A vector has magnitude and direction.

Examples: A car is moving at 55 mph to the northeast.
. . . . . . . . A ball is thrown at 30 ft/s at an angle of 50° to the horizontal.
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outermeasure
 Post subject: Re: question
PostPosted: Sun, 3 Jul 2011 01:08:15 UTC 
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Soroban wrote:
Hello, shaharhada1!

Quote:
What is the difference between a scalar and a vector?

A scalar is a numerical quantity. .It has magnitude (size) only.

Examples: A car is moving at 55 miles per hour.
. . . . . . . . A ball is thrown at 30 feet per second.


A vector has magnitude and direction.

Examples: A car is moving at 55 mph to the northeast.
. . . . . . . . A ball is thrown at 30 ft/s at an angle of 50° to the horizontal.


That explanation is only true if the field is (\mathbb{R} or subfields of \mathbb{R}) and the vector space is a normed space. It doesn't make sense when it is, e.g., \mathbb{C} as a \mathbb{C}-vector space, or the space of rational functions of n variables over a field k of positive characteristic.

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: I have a question
PostPosted: Tue, 5 Jul 2011 23:21:45 UTC 
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shaharhada1 wrote:
Is k a vector?
if it is, what the difference between it to scalar that called M?


If that was directed at me, I meant what class are you learning about vectors in and what kinds of things are they being used for? It doesn't seem like you are really asking about true, general vectors.

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