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Matrices satisfying certain relations 
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#1
Nov2112, 09:15 AM

P: 56

How do you find matrices a,b,c satisfying
a=b*c*b^1 b=c*a*c^1 c=a*b*a^1 ? 


#2
Nov2112, 09:37 AM

P: 15

If you know what's diagonalization, you can skip this.
For a to be diagonalizable, A=PDP^1, where P is an invertible matrix whose columns are A's eigenvector (order of these columns doesn't matter). C is a diagonal matrix that has all A's eigenvalues So for a 3x3 diagonalizable matrix D= λ1 0 0 0 λ2 0 0 0 λ3 λ{1,2,3} are A's eigenvalues P= [v1 v2 v3] v{1,2,3} are A's eigenvectors From those 3 equations in your post you can see that a, b and c have to be all diagonal matrices. Also, a has to have b's eigenvalues, b has to have c's eigenvalues and c has to have a's eigenvalues. And of course, a has to have c's eigenvectors... etc Not sure how i would start solving this, but I hope this helps. 


#3
Nov2212, 03:33 AM

P: 144




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