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Matrix diagonalization

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Definition of matrix diagonalization
Definition of diagonalizable matrix
An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.
An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.
Diagonalizability requires splitting and equality of geometric and algebraic multiplicities
A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.
An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).
An n-by-n matrix with n distinct eigenvalues is diagonalizable.
Real block form and complex diagonalization for a 2-by-2 matrix

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Definition of diagonalizable matrix

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An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).Close match
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An n-by-n matrix with n distinct eigenvalues is diagonalizable.Close match
An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.Close match
Definition of orthogonally diagonalizable matrixClose match
A linear transformation is diagonalizable if there is a basis such that each element is an eigenvector of the transformation.Close match
A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.Close match
Definition of block diagonal matrixClose match
Definition of skew-symmetric matrixClose match
Real block form and complex diagonalization for a 2-by-2 matrixClose match
Commuting diagonalizable and nilpotent decomposition over the complex numbersClose match
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Definition of conjugate of a matrixRelated
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