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Definition of (algebraic) multiplicity of an eigenvalue
Definition of geometric multiplicity of an eigenvalue
An n-by-n complex matrix has n eigenvalues counting multiplicity

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Definition of geometric multiplicity of an eigenvalue

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Definition of (algebraic) multiplicity of an eigenvalueClose match
MultiplicityClose match
The dimension of a eigenspace is less than or equal to the (algebraic) multiplicity of the eigenvalue.Close match
An n-by-n complex matrix has n eigenvalues counting multiplicityClose match
Definition of eigenspace of a linear transformationClose match
An eigenspace of a matrix is a nontrivial subspace.Close match
Definition of eigenvalue of a matrixClose match
Diagonalizability requires splitting and equality of geometric and algebraic multiplicitiesClose match
Definition of eigenspace of a matrixRelated
EigenspacesRelated
The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.Related
The eigenvalues of a power of a matrix are the power the eigenvalues.Related
A matrix and its transpose have the same eigenvalues/characteristic polynomial.Related
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.Related
The eigenspace of a linear transformation is a nontrivial subspace.Related
Definition of matrix-scalar multiplicationRelated
Definition of matrix multiplication in terms of column vectorsRelated
Example of multiplying nonsquare matricesRelated
Example of multiplying matricesRelated
Matrix-scalar multiplication is commutativeRelated

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