The discussion focuses on calculating the expression trace(p^4 - p^3) for a 2x2 complex matrix P, given that trace(P) = 1 and det(P) = -6. The eigenvalues of the matrix are determined to be a = (1 + i√23)/2 and b = (1 - i√23)/2. Using the properties of traces, it is established that trace(p^4 - p^3) can be computed as trace(p^4) - trace(p^3), leveraging the eigenvalues to derive the necessary values.
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ajayguhan said:Homework Statement
Let P be 2x2 complex matrice such that trace(p)=1 det(p)=-6 then trace(p^4-p^3) equals what...?
Homework Equations
Is there any formula for trace(A^n)
The Attempt at a Solution
Let the two eigen values be a,b
a+b=1 a*b= -6 solving we get a=(1+i√23)/2 and b =(1-i√23)/2
Trace(p^4-p^3)=trace(p^4)-trace(p^3)