Answer to Question #46093 in Engineering for Sapna

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. (3)
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). (5)
c) Which of the following matrices are Hermitian and which are Unitary? Justify your
answer. (4)
A =
2
4
1 i 0
i 1 1 i
0 1 + i 2
3
5
; B =
2
4
1
p
2
0
1
p
2
0 1 0
p
2i 0
p
2i
3
5