Diagonalize operator A by matrix S

Context: Graduate
Thread starter Abrar Quadery
Start date Sep 20, 2010
Tags

Matrix Operator

Join the discussion

Registration is free. Ask a follow-up in this thread, or start your own.

1 reply · 2K views

Abrar Quadery

Thread starter
Sep 20, 2010

Suppose, i want to diagonalize operator A by matrix S (A'= S^\\dagger A S). Do i need to form S from "NORMALIZED" eigenvectors? I checked and found that even S formed from not-normalized eigenvectors works.

Discussion

Physics news on Phys.org

Optimized magnetic pulses could cut memory switching energy by several orders of magnitude
Diamond's newfound defect may tame vibrations that hinder quantum light sources
New photonic platform offers a four-lane highway for light

Parlyne

Sep 20, 2010

If S isn't normalized, you will get a diagonal matrix. However, the diagonal elements of the matrix will not be the eigenvalues of A.

Diagonalize operator A by matrix S

Discussion

Undergrad ##r-##independent angular momentum in quantum mechanics

High School Seemingly odd quantum tunneling

Undergrad What empirical observation supports the axiom of continuous spacetime?

Graduate Exact symmetry, quantum states, and symmetric dynamics

High School Question about entanglement and spacetime

Graduate Avalanche photon detectors

Undergrad A Dataset & Signal Analysis Interpretation of Quantum Mechanics

High School Two/three photon absorption chemical substance producing photons for electricity generation

Graduate Numerical implementation of creation and annhilation operators in the SSH model

Undergrad Far off resonant Rabi oscillations in a 2 level system

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

Diagonalize operator A by matrix S

Discussion

Similar threads

Undergrad Density matrix representation of a density operator

Graduate Diagonalization of 2x2 Hermitian matrices using Wigner D-Matrix

Graduate How to numerically diagonalize a Hamiltonian in a subspace?

Undergrad Interferences (with diagonal density matrix)

Graduate Matrix representation of a unitary operator, change of basis

Graduate QFT S-matrix explanations are incomprehensible

Graduate Can a Non-Diagonal Hermitian Matrix be Diagonalized Using Unitary Matrix?

Undergrad Matrix Representation of the Angular Momentum Raising Operator

How can a diagonalising matrix be unitary?

Undergrad Matrix element involving raising/lowering operators