multiplicity of eigenvalues
(1 hours to learn)
The characteristic polynomial of a matrix may have repeated roots. If this is the case, the geometric multiplicity of a given eigenvalue (the dimension of the corresponding eigenspace) may be less than the algebraic multiplicity. This property determines whether a matrix is diagonalizable, and it is relevant to the solutions of differential equations.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
Location: Section "Properties of eigenvalues and eigenvectors," subsection "Multiplicities of eigenvalues"
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 9.2, "Eigenvalues, eigenvectors, and applications," subsection 9.2.2, "Diagonalizability," pages 429-433
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