Algebraic and Geometric Multiplicity of Eigenvalues | Linear Algebra

We define the algebraic multiplicity of eigenvalues and the geometric multiplicity of eigenvalues. We'll see an example and an important theorem. The algebraic multiplicity of an eigenvalue is the number of times the eigenvalue appears in the factored form of the characteristic polynomial when written as a product of linear factors. The geometric multiplicity of an eigenvalue is the dimension of the corresponding eigenspace. #linearalgebra

Eigenvalues and Eigenvectors:    • Eigenvectors and Eigenvalues of a Mat...  
Eigenspaces and their Bases:    • Eigenspaces and their Bases | Linear ...  

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0:00 Intro
0:37 Definition of Algebraic and Geometric Multiplicities
1:22 Example of Algebraic and Geometric Multiplicities
3:57 Diagonalizability and Multiplicity Theorem
5:31 Conclusion

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