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normal matrix
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Normala matrico
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matrix that commutes with its conjugate transpose
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This can be seen by looking at the diagonal entries of A*A and AA*, where A is a normal, triangular matrix.
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A square matrix is diagonal if and only if it is triangular and normal.
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If the matrix A has multiple eigenvalues, or is close to a matrix with multiple eigenvalues, then its Jordan normal form is very sensitive to perturbations.
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Using the Jordan normal form, one can prove that every square real matrix can be written as a product of two real symmetric matrices, and every square complex matrix can be written as a product of two complex symmetric matrices.
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Real skew-symmetric matrices are normal matrices (they commute with their adjoints) and are thus subject to the spectral theorem, which states that any real skew-symmetric matrix can be diagonalized by a unitary matrix.
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