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Built-in Mathematica Symbol

RealBlockDiagonalForm

RealBlockDiagonalForm
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.

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With RealBlockDiagonalForm->False, complex values can be generated on matrix diagonals from SchurDecomposition and related functions.

With the default setting RealBlockDiagonalForm->True, complex values are replaced by 2×2 blocks of real values.

EXAMPLES

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Basic Examples (1)

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:

m is a matrix with two real and two complex eigenvalues:

In[1]:=

Out[1]=

With RealBlockDiagonalForm->False, the result is complex upper-triangular:

In[2]:=

In[3]:=

Out[3]//MatrixForm=

With RealBlockDiagonalForm->True, there are real 2×2 blocks along the diagonal:

In[4]:=

In[5]:=

Out[5]//MatrixForm=