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Problem
#69283

Linear Algebra : Linear Functionals

Now let V be the space of all 2x2 matrices over the field F and let P be a fixed 2x2 matrix. Let T be the linear operator on V defined by T(A) =PA . Prove that tr(T)=2tr(P).  

From a previous exercise we know that similar matrices have the same trace. Thus we can define the trace of a linear operator on a finite-dimensional space to be the trace of any matrix, which represents the operator in an ordered basis. This is well defined since all such representing matrices for one operator are similar.

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From a previous exercise we know that similar matrices have the same
trace. Thus we can define the trace of a linear operator on a
finite-dimensional space to be the trace of any matrix, which represents
the operator in an ordered basis. This is well defined since all such
representing matrices for one operator are similar.



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Linear functionals are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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Yupei Xiong, PhD - 4.8/5
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