A∈Rnxn,非奇异P∈Rnxn,A=PJP-l。其中 EE+Z+云2+…+ rn-1 1 x 易知 于是 A=ePJp-=Pep-1, →e2ip=Pe.∀A ∈ R n×n, ∃ ö¤…P ∈ R n×nß−−3 A = P JP −1"Ÿ• J = J1 J2 . . . Jm , Ji = λi 1 λi . . . . . . 1 λi ni×ni P Ji = λiE + Z = λi λi . . . λi + 0 1 0 . . . . . . 1 0 K e xJi = e λixE(E + Z + x 2 2! Z 2 + · · · + x ni−1 (ni − 1)!Z ni−1 ) = e λix 1 x x 2 2! · · · x ni−1 (ni−1)! 1 x x ni−2 (ni−2)! . . . . . . . . . x 1 ¥ e xJ = e xJ1 e xJ2 . . . e xJm . u¥ e xA = e xP JP −1 = P exJP −1 , =⇒ e xAP = P exJ