Let V be a normal operator on a finite dim complex inner product space V use the spectral theorem?

decomposition λ_1t_1+ λ_2t_2+...+ λ_kt_k of t prove following results
a. if g polynomial g(t)= sum 1=1 k of g( λ_i)(t_i)
b. if t^n=t_0 n t=t_0
c. let u linear operator on v. u commutes t if , if u commutes each t
d. there exists normal operator u on v such u^2=t
e.t invertible if , if λ_i not equal 0 1<+i<=k
f. t porjection if , if every eigenvalue of t 1 or 0
g. t=-t* if , if every λ_i imaginary number

decomposition λ_1t_1+ λ_2t_2+...+ λ_kt_k of t prove following results a. if g polynomial g(t)= sum 1=1 k of g( λ_i)(t_i) b. if t^n=t_0 n t=t_0 c. let u linear operator on v. u commutes t if , if u commutes each t d. there exists normal...

Science & Mathematics Mathematics Next