InterviewSolution
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InterviewSolution
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If `A=((1,2),(0,1))` `P=((cos theta , sin theta),( -sin theta, cos theta))`, `Q=P^T AP` find `PQ^(2014)P^T` |
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Answer» `Q=P^TAP` `QP^T=P^TAPP^T` `QP^T=P^TA` `PQ^2014 P^T=PQ^2013QP^T=PQ^2013P^TA` `=PQ^2012QP^TA=PQ^2012P^TA^2` `=PW^2011QP^TA^2=PQ^2011P^TA^3` `=PP^TA^2014=IA^2014=A^2014`. `A=[[1,2],[0,1]]` `A^2=[[1,2],[0,1]]*[[1,2],[0,1]]` `=[[1,4],[0,1]]` `A^3=[[1,2],[0,1]]*[[1,2],[0,1]]*[[1,2],[0,1]]` `A^3=[[1,6],[0,1]]` `A^2014=[[1,4028],[0,1]]`. |
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