3)

A)

there is a lenear transformation T:V->V in inner product

it is given that

. prove that T is positive definite and find every posible

eigenvalue of T

?

B)

we define

write the formula as a sum of squares,find the rank and signature of q

?

regarding A:

the book definition is:

a matrices which is hermitic A^{*}=A and for every vector and k of our choosing

i dont know how to use it here

regarding B :

in the books definition a signature is \sigma=\pi-\mu

is the number of positive members=2

is the number of negative members =4

i got

??

in order to find the rank i need to find representative matrices in

and the rest stays the same

i got here 5 member in power 2

but my matrices is 4x4 i cant have 5 members in the diagonal of 4x4 matrices

??