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olivertan92
 Post subject: Row reduce this !
PostPosted: Mon, 21 May 2012 05:59:09 UTC 
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i have been cracking my head over this matrix for almost 20mins and i stll cant find an aswer to it.

a = [k 1 1 1
1 k 1 1
1 1 k 1]

thanks
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outermeasure
 Post subject: Re: Row reduce this !
PostPosted: Mon, 21 May 2012 06:03:43 UTC 
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olivertan92 wrote:
i have been cracking my head over this matrix for almost 20mins and i stll cant find an aswer to it.

a = [k 1 1 1
1 k 1 1
1 1 k 1]

thanks


Divide and conquer.

If k=1, then ...
Otherwise ...

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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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olivertan92
 Post subject: Re: Row reduce this !
PostPosted: Mon, 21 May 2012 06:22:46 UTC 
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I could only do one step.. :(

k 1 1 1
0 1/k-k 1/k-1 1/k-1
0 1/k-1 1/k-k 1/k-1


how do i go on and simplify the last row?
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Shadow
 Post subject: Re: Row reduce this !
PostPosted: Mon, 21 May 2012 06:56:43 UTC 
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olivertan92 wrote:
I could only do one step.. :(

k 1 1 1
0 1/k-k 1/k-1 1/k-1
0 1/k-1 1/k-k 1/k-1


how do i go on and simplify the last row?


You need some parentheses methinks.

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olivertan92
 Post subject: Re: Row reduce this !
PostPosted: Mon, 21 May 2012 07:20:31 UTC 
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what? parentheses methink? tried google-ing it and nothing maths related showed up. Could someone like point me in the right direction.. thanks
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Shadow
 Post subject: Re: Row reduce this !
PostPosted: Mon, 21 May 2012 07:30:52 UTC 
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olivertan92 wrote:
what? parentheses methink? tried google-ing it and nothing maths related showed up. Could someone like point me in the right direction.. thanks


methinks = "I believe"

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