Question

a) Check whether the forms 2x^2+3y^2+5z^2−4xz−6yz and 4x^2+3y^2+z^2−6xy−2xz are orthogonally equivalent.
b) Use Gram-Schmidt orthogonalisation process to find an orthonormal basis for the subspace of C^4 generated by the vectors (1,i,0,−i), (−i,0,1,2) and (0,−i,1,1).
c) Which of the following matrices are Hermitian and which are Unitary? Justify your answer.

A= 1 i 0 B= 1/√2 0 -1/√2
-i 1 1-i 0 1 0
0 1+i 2 √2i 0 √2i