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aliya
 Post subject: matrix addition to matrix multiplication
PostPosted: Sun, 8 Aug 2010 17:40:08 UTC 
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Suppose two matrices A and B . i want to transform matrix addition to matrix multiplication. e.g A+B into A.B.
Can anybody please tell me of any way i can do it ,except exponentiation? exponentiation gives an infinite answer.
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outermeasure
 Post subject: Re: matrix addition to matrix multiplication
PostPosted: Sun, 8 Aug 2010 18:23:45 UTC 
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aliya wrote:
Suppose two matrices A and B . i want to transform matrix addition to matrix multiplication. e.g A+B into A.B.
Can anybody please tell me of any way i can do it ,except exponentiation? exponentiation gives an infinite answer.


You can't in general.

_________________
\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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