# Matrices satisfying certain relations

by neginf
Tags: matrices, relations, satisfying
 Share this thread:
 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 ?
 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.
P: 144
 Quote by aija From those 3 equations in your post you can see that a, b and c have to be all diagonal matrices.
Hi Aija, your statement above is just wrong. From those 3 equations, you should immeditately observe the solution a=b=c=M, where M is any invertible matrix, and the "problem" is to determine the remaining solutions, if any.

 Related Discussions Calculus & Beyond Homework 1 Linear & Abstract Algebra 1 Calculus & Beyond Homework 15 General Physics 16 Advanced Physics Homework 2