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.
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.
Details
- 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
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:
See Also
History
Text
Wolfram Research (2008), RealBlockDiagonalForm, Wolfram Language function, https://reference.wolfram.com/language/ref/RealBlockDiagonalForm.html.
CMS
Wolfram Language. 2008. "RealBlockDiagonalForm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RealBlockDiagonalForm.html.
APA
Wolfram Language. (2008). RealBlockDiagonalForm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RealBlockDiagonalForm.html
BibTeX
@misc{reference.wolfram_2025_realblockdiagonalform, author="Wolfram Research", title="{RealBlockDiagonalForm}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/RealBlockDiagonalForm.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_realblockdiagonalform, organization={Wolfram Research}, title={RealBlockDiagonalForm}, year={2008}, url={https://reference.wolfram.com/language/ref/RealBlockDiagonalForm.html}, note=[Accessed: 17-November-2025]}