Question

设三界是对称矩阵A满足A^3-3A^2+5A-3E=0,则A的三个特征值为?

Answer 1

特征方程为

r³-3r²＋5r-3=0

r³-r²-2r²＋2r＋3r-3=0

r²(r-1)-2r(r-1)+3(r-1)=0

(r-1)(r²-2r+3)=0

r1=1或

r²-2r+3=0

(r-1)²=-2

r2,3=1±√2i

即特征值为

λ1=1,λ2,3=1±√2i