add hermitian_decomposition method #39200
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I really dislike these apply-suggestion-commits with a completely useless commit message. Could you please squash and rebase? It makes it easier to see which changes have been done and looking through the logs much later. |
add hermitian_decomposition method given a Hermitian matrix U, returns a matrix A such that U = AA* use translated GAP source code for BaseChangeCanonical Co-Authored-By: Travis Scrimshaw <[email protected]>
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Sure. I agree, the commit messages are pretty useless. I've squashed the commits here. Which branch should I rebase on? I rebased PR#38455 on this one (PR#39200) already. |
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Thanks. Sorry, I misspoke slightly, I meant force-push.You will need to rebase #38455 again though… |
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I don't think this handles the 1x1 case, so I'll add a fix. |
Co-authored-by: Travis Scrimshaw <[email protected]>
Co-authored-by: Travis Scrimshaw <[email protected]>
Co-authored-by: Travis Scrimshaw <[email protected]>
Co-authored-by: Travis Scrimshaw <[email protected]>
Co-authored-by: Travis Scrimshaw <[email protected]>
…alters/sage into hermitian_decomposition
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@tscrim How do I squash these commits given there's a merge commit? We may've done this before, but I don't see how. |
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I would just rebase the entire branch over the latest |
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| A = B^* B, | ||
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| where `B^\ast` is the conjugate-transpose. |
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| where `B^\ast` is the conjugate-transpose. | |
| where `B^*` is the conjugate-transpose. |
Let's be consistent. ;)
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| A conjugate-symmetric version of Gaussian elimination. | ||
| This is a translation of ``BaseChangeToCanonical`` from | ||
| the GAP ``forms`` for a Hermitian form. |
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| the GAP ``forms`` for a Hermitian form. | |
| the GAP ``forms`` package for a Hermitian form. |
| row += 1 | ||
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| # Look for a non-zero element on the main diagonal, starting from `row` | ||
| i = row - 1 # Adjust for zero-based indexing in Sage |
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I don't think this is possible as we mutate i compared to row.
Given a Hermitian matrix$U$ over $GF(q^2)$ , returns a matrix $A$ such that $U = AA^\ast$ , where $^\ast$ denotes conjugate-transpose.
Note that the Cholesky decomposition is meant for characteristic zero, and also only returns a lower/upper triangular matrix.
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