The algebraic multiplicity of an eigenvalue λ is the number of times that λ repeats as a solution to the characteristic equation det(A-λI)=0. The geometric multiplicity of an eigenvalue λ is the number of linearly independent eigenvectors associated with λ, which is determined as the difference between the number of unknowns and the rank of the matrix A- λI.

1. Prepared by: YASH PATEL

3.  If the eigen value λ of the equation
det(A-λI)=0 is repeated n times then n is
called the algebraic multiplicity of λ.

4.  The number of linearly independent eigen
vectors is the difference between the number
of unknowns and the rank of the
corresponding matrix A- λI and is known as
geometric multiplicity of eigen value λ.

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