The algebraic multiplicity of an eigenvalue is its multiplicity as a root of the characteristic polynomial. In Jordan form it is the sum of the sizes of all blocks carrying that eigenvalue.
Ancestors (7)
Incoming links (45)
- Characteristic polynomial from traces of powers
- Defective matrix
- Diagonalizability depends on the field
- Diagonalizable matrix
- Eigenvalue addition in a common eigenbasis
- Eigenvalue deflation by an invariant subspace
- Gershgorin eigenvalue counting
- Invertible anticommuting matrices have even dimension and zero traces
- Matrix similarity invariants
- Matrix trace
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- Reciprocal spectrum of a symplectic matrix
- Repeated eigenvalues in the Cayley-Hamilton theorem
- Same eigenvalues do not imply similarity
- Simple eigenvalue
- Simple spectrum
- Spectrum of an all-ones matrix
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