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Intro
Definition of eigenvalues and eigenvectors
Properties of eigenvalues and eigenstates
What can we say about the extra degree of freedom?
The identity operator
Explicit representations of eigenstates and eigenoperators
Characteristic equation and eigenvalues
Hermitian and unitary operators
Normalized eigenstates
Outro
Introduction
Linear transformations
Definition of eigenvectors
Eigenvalues and eigenvectors dictate the nature of the transformation for the entire object
Applying the transformation
Eigenvectors not necessarily at 90 degrees
Notation for eigenvectors
Sum of eigenvectors
Multiply each eigenvector by its corresponding eigenvalue
Conclusion
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