67 The Matrix Package

This chapter describes functions which may be used to construct and investigate the structure of matrix groups defined over finite fields.

Subsections

1. Aim of the matrix package
2. Contents of the matrix package
3. The Developers of the matrix package
4. Basic conventions employed in matrix package
5. Organisation of this manual
6. GModule
7. IsGModule
8. IsIrreducible for GModules
9. IsAbsolutelyIrreducible
10. IsSemiLinear
11. IsPrimitive for GModules
12. IsTensor
13. SmashGModule
14. HomGModule
15. IsomorphismGModule
16. CompositionFactors
17. Examples
18. ClassicalForms
19. RecogniseClassical
20. ConstructivelyRecogniseClassical
21. RecogniseMatrixGroup
22. RecogniseClassicalCLG
23. RecogniseClassicalNP
24. InducedAction
25. FieldGenCentMat
26. MinimalSubGModules
27. SpinBasis
28. SemiLinearDecomposition
29. TensorProductDecomposition
30. SymTensorProductDecomposition
31. ExtraSpecialDecomposition
32. MinBlocks
33. BlockSystemFlag
34. Components of a $G$-module record
35. ApproximateKernel
36. RandomRelations
37. DisplayMatRecord
38. The record returned by RecogniseMatrixGroup
39. DualGModule
40. InducedGModule
41. PermGModule
42. TensorProductGModule
43. ImprimitiveWreathProduct
44. WreathPower
45. PermGroupRepresentation
46. GeneralOrthogonalGroup
47. OrderMat -- enhanced
48. PseudoRandom
49. InitPseudoRandom
50. IsPpdElement
51. SpinorNorm
52. Other utility functions
53. References