1)

there is

A.we define by for every and in

does f define inner product in ?

how i tried:

in the book by definition inner product is following these rules:

(u,v)=(v,u)

(u+v,w)=(u,w)+(v,w)

(ku,v)=k(u,v)

i dont know how to apply these rules here

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B.find a simetric matrices B so

(clue: use cayley-Hamilton law)

?

how i tried:

hamilton law say that the representative matrice turns to zero the minimal polinomial M(A)=0

any guidence

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