Show that the tensor product of two positive operators is positive.

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genius_generous answered 1 year ago

prove that positive operators have unique positive square root

Show that the affine connection is not a true tensor (general relativity/cosmology)

If two operators do not commute, show that we cannot simultaneously diagonalise them .

a) prove the derivative of a tensor is a tensor b.) prove that the the direct...

a) prove the derivative of a tensor is a tensor b.) prove that the the direct product of two tensors is a tensor

(a) Show that if operators have common eigenstates they will commute. (b) Show also that the...

(a) Show that if operators have common eigenstates they will commute. (b) Show also that the opposite is true too: if two operators commute they have common eigenstates.

Show that Christoffel symbols do not transform like a tensor. And, how does the determinant of...

Show that Christoffel symbols do not transform like a tensor. And, how does the determinant of the metric tensor transform general under coordinate transformation?

Prove that the covariant derivative of an arbitrary tensor is a tensor of which the covariant...

Prove that the covariant derivative of an arbitrary tensor is a tensor of which the covariant order exceeds that of the original by one.

What is a tensor itself? What is tensor notation used for? What is differencce between a...

What is a tensor itself? What is tensor notation used for? What is differencce between a tensor and a vector?

Show that Hermitian operators have real eigenvalues. Show that eigenvectors of a Hermitian operator with unique...

Show that Hermitian operators have real eigenvalues. Show that eigenvectors of a Hermitian operator with unique eigenvalues are orthogonal. Use Dirac notation for this problem.

(a) Show that the diagonal entries of a positive definite matrix are positive numbers. (b) Show...

(a) Show that the diagonal entries of a positive definite matrix are positive numbers. (b) Show that if B is a nonsingular square matrix, then BTB is an SPD matrix.(Hint. you simply need to show the positive definiteness, which does requires the nonsingularity of B.)

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