- #1
dyn
- 773
- 62
Apologies if this should be in homework section but I thought it best suited here. Been revising past papers but with no solutions. the following questions all require just a true or false answer. Any help or confirmation of my answers would be appreciated.
1 - every N x N matrix has N eigenvectors T/F ?
I think false because there would be infinitely many as any eigenvector can be multiplied by any scalar
2 - Operator R is diagonalizable where R = exp( i pi Sx /hbar) where Sx is the x spin operator
I think false because the x spin operator is not diagonal
3 - product of 2 unitary operators is a unitary operator T/F ?
i have no idea
4 - the exponential of a hermitian operator is a unitary operator T/F ?
I have no idea
The following questions all relate to finite dim complex vector space V
5 - the matrix representation of the identity operator is basis dependent T/F ?
i think false
6 - An orthogonal projector ( to a lower dim subspace) is neither injective nor surjective in V T/F ?
i think its not surjective , not sure about injective
1 - every N x N matrix has N eigenvectors T/F ?
I think false because there would be infinitely many as any eigenvector can be multiplied by any scalar
2 - Operator R is diagonalizable where R = exp( i pi Sx /hbar) where Sx is the x spin operator
I think false because the x spin operator is not diagonal
3 - product of 2 unitary operators is a unitary operator T/F ?
i have no idea
4 - the exponential of a hermitian operator is a unitary operator T/F ?
I have no idea
The following questions all relate to finite dim complex vector space V
5 - the matrix representation of the identity operator is basis dependent T/F ?
i think false
6 - An orthogonal projector ( to a lower dim subspace) is neither injective nor surjective in V T/F ?
i think its not surjective , not sure about injective