- #1
neomasterc
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Homework Statement
Prove I=T1+T2+...+Tk
Where Ti=pi(T)
Homework Equations
T is kxk
pi(x)=(x-c1)...(x-ck) is the minimal polynomial of T.
pi=[itex]\pi[/itex]i(x)/[itex]\pi[/itex]i(ci)
[itex]\pi[/itex]i=[itex]\pi[/itex](x)/(x-ci)
To evaluate these functions at a matrix, simply let ci=ciI
The Attempt at a Solution
From lagrange interpolation, f=Ʃf(x)pi(x)
so 1=Ʃpi(x)