Mathematics · University
Eigenvectors and diagonalization · revision notes
Av=λv requires a nonzero vector v.
Key ideas and conditions
Eigenpair
Av=λv requires a nonzero vector v.
Diagonalization
A=PDP⁻¹ exists when there is a basis of eigenvectors over the chosen field.
Repeated eigenvalues
Algebraic multiplicity does not guarantee enough independent eigenvectors.
Symmetric matrices
A real symmetric matrix has an orthonormal eigenbasis over the reals.
Explain without looking
- A real symmetric matrix always admits what decomposition?
- Explain why diagonalization helps calculate A^n.
Further reading and review references
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