Inner Product Spaces: Normal & Self Adjoint?

hitmeoff · May 31, 2010

An inner product space can be both normal and self adjoint, correct?

hitmeoff · Jun 1, 2010

Nevermind, but I got another question, since self-adjoint means that and I.P.S. is equal to it Adjoint, wouldn't all self-adjoint I.P.S. by default be normal?

HallsofIvy · Jun 1, 2010

I have no idea what you are talking about. "Self adjoint" applies to a linear operator on an inner product space, not to the space itself.

Are you asking if "self-adjoint" and "normal" are the same for a linear operator on an inner product space?

Inner Product Spaces: Normal & Self Adjoint?

Discussion

Undergrad The vector to which a dual vector corresponds

Undergrad Spinor calculus

Undergrad Matrix representation of rank-2 spinors

Undergrad Looking for a paper about spinors

Undergrad Why are these cycles disjoint and of equal length?

On the Moore–Penrose inverse from a banal linear algebra viewpoint

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Inner Product Spaces: Normal & Self Adjoint?

Discussion

Similar threads

Graduate Hilbert-adjoint operator vs self-adjoint operator

Undergrad Doubt about proof on self-adjoint operators.

Undergrad Can Normal Matrices Be Non-Self-Adjoint?

Amy's question at Yahoo Answers (Self adjoint operator)

Graduate Proving Self-Adjointness in Finite-Dimensional Vector Spaces with Inner Products

Self Adjoint and Unitary Transformations

Graduate Introducing Inner Product Spaces: Real Impact Examples

Introducing Inner Product Spaces: Real-World Examples

Graduate Self Adjoint and Anti-Self Adjoint questoin

Linear algebra inner products, self adjoint operator,unitary operation