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is an option for SchurDecomposition and related functions which specifies whether 2×2 blocks of real values should be used on matrix diagonals in place of complex values.
m is a matrix with two real and two complex eigenvalues:
With RealBlockDiagonalForm->False, the result is complex upper triangular:
With RealBlockDiagonalForm->True, there are real 2×2 blocks along the diagonal: