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smoothman
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any ideas on how to go about conducting these please. i will attempt them once i have a clear idea on how to do this. thanks :)
let V be the vector space of polynomials over C of degree <= 10 and let
"D: V -----> V" be the linear map defined by
D(f) = df/dx
show
(1) D^11=0
(2) deduce 0 is the only eigenvalue of D
(3) find a basis for the generalised eigenspaces v1(0), v2(0), and v3(0).
let V be the vector space of polynomials over C of degree <= 10 and let
"D: V -----> V" be the linear map defined by
D(f) = df/dx
show
(1) D^11=0
(2) deduce 0 is the only eigenvalue of D
(3) find a basis for the generalised eigenspaces v1(0), v2(0), and v3(0).