Basic Examples (1) 

Return the diagonalized matrix for a matrix:

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Scope (2) 

DiagonalizeMatrix works with complex-valued matrices:

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DiagonalizeMatrix works with matrices containing symbolic elements:

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Properties and Relations (2) 

When the matrix is diagonalizable, DiagonalizeMatrix returns the diagonal matrix from JordanDecomposition:

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The Eigenvalues of the matrix appear along the diagonal of DiagonalizeMatrix:

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Possible Issues (2) 

The function returns unevaluated when the matrix is not square:

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The function returns unevaluated when the matrix is not diagonalizable:

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For non-diagonalizable square matrices, a form that is "almost" diagonalized exists, having zeros and ones on the superdiagonal and zeros elsewhere than the main diagonal. It can be found using JordanDecomposition:

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