| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/repndecomp/lib/ (GAP Algebra Version 4.15.1©) Datei vom 12.8.2025 mit Größe 1 kB |
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Quelle block_diagonalize.gd Sprache: Shell |
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#! @Chapter Computing decompositions of representations #! @Section Block diagonalizing #! Given a representation $\rho : G \to GL(V)$, it is often desirable #! to find a basis for $V$ that block diagonalizes each $\rho(g)$ with #! the block sizes being as small as possible. This speeds up matrix #! algebra operations, since they can now be done block-wise. #! @Arguments rho #! @Returns Basis for $V$ that block diagonalizes $\rho$. #! @Description Let $G$ have irreducible representations $\rho_i$, #! with dimension $d_i$ and multiplicity $m_i$. The basis returned by #! this operation gives each $\rho(g)$ as a block diagonal matrix #! which has $m_i$ blocks of size $d_i \times d_i$ for each $i$. DeclareGlobalFunction( "BlockDiagonalBasisOfRepresentation" ); #! @Arguments rho #! @Returns Representation of $G$ isomorphic to $\rho$ where the #! images $\rho(g)$ are block diagonalized. #! @Description This is just a convenience operation that uses <Ref #! Attr="BlockDiagonalBasisOfRepresentation" /> to calculate the basis #! change matrix and applies it to put $\rho$ into the block #! diagonalised form. DeclareGlobalFunction( "BlockDiagonalRepresentation" ); DeclareGlobalFunction( "BasisChangeMatrixSimilar" );
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2026-11-04