Algebraic Multiplicity

#incomplete

Related: Geometric Multiplicity

Algebraic multiplicity () of the eigenvector, , is the multiplicity of as a root of the characteristic polynomial .

For example, given a matrix , that when finding the eigenvalues via the determinant of a matrix yields the characteristic polynomial and then after completing the square we find thus the eigenvalue of matrix is twice, thus the eigenvalue has an algebraic multiplicity of 2 as it appears twice.

revise above example

See 4-Sect 4.7 Defective Matrix

Cited:

• https://people.math.carleton.ca/~kcheung/math/notes/MATH1107/wk10/10_algebraic_and_geometric_multiplicities.html