Chapter 3 8 7.Matrix Function of Scalar Pu(t) P12(t) Pi(t) P:R→Ra P(t)= P21(t) P22(t) or P2m() … Pa(t)Pn2(1) Pnn()J」 Furthermore,Matrix Function of Vector Pu(X) P12(X) Pi(X) P:R'→R or P(X)= P21(X) P22(X) p2m(X) X= … P(X) P2(X) P(X) Example 2x1+3x22+hx3 f(X)= sin x +cos x3 where log x2 f(X)=2x1+3x,2+hx; x f2 (X)=sim x+cosx; and X= 2 f;(X)=log x2 X3 7. Matrix Function of Scalar n m R R  P :  or              ( ) ( ) ( ) ... ... ... ... ( ) ( ) ... ( ) ( ) ( ) ... ( ) ( ) 1 2 2 1 2 2 2 1 1 1 2 1 p t p t p t p t p t p t p t p t p t t n n n m m m P Furthermore, Matrix Function of Vector r n m R R  P :  or              ( ) ( ) ... ( ) ... ... ... ... ( ) ( ) ... ( ) ( ) ( ) ... ( ) ( ) 1 2 2 1 2 2 2 1 1 1 2 1 X X X X X X X X X P X n n n m m m p p p p p p p p p              r x x x ... 2 1 X Example               2 1 3 3 2 1 2 log sin cos 2 3 ln ( ) x x x x x x f X where 3 2 1 1 2 f ( X )  2 x  3 x  ln x 2 1 3 f ( X )  s in x  c o s x 3 2 f ( X )  lo g x and            3 2 1 X x x x Chapter 3 8