A First Course in Linear Algebra · Problem CB.C30

Representations — Robert Beezer

Mathematics — Linear Algebra · eigenvectors-basis-polynomial-linear-transformation

Problem

Find a basis for the vector space P3P_3 composed of eigenvectors of the linear transformation TT. Then find a matrix representation of TT relative to this basis. T:P3→P3,T(a+bx+cx2+dx3)=(a+c+d)+(b+c+d)x+(a+b+c)x2+(a+b+d)x3T: P_3 \to P_3, \quad T\left(a+bx+cx^2+dx^3\right) = (a+c+d)+(b+c+d)x+(a+b+c)x^2+(a+b+d)x^3

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