# Matrix Groups over Q and Z

- [Overview](Overview.md)

- [Invariant Forms](forms.md)

  - [`PositiveDefiniteForm(G): GrpMat → Mtrx`](forms.md#function-grpmatqz-positivedefiniteform)

  - [`InvariantForms(G): GrpMat → [ AlgMatElt ]`](forms.md#function-invariantforms-grpmat)

  - [`SymmetricForms(G): GrpMat → [ AlgMatElt ]`](forms.md#function-symmetricforms-grpmat)

  - [`AntisymmetricForms(G): GrpMat → [ AlgMatElt ]`](forms.md#function-antisymmetricforms-grpmat)

  - [`InvariantForms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]`](forms.md#function-invariantforms-grpmat-rngintelt)

  - [`SymmetricForms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]`](forms.md#function-symmetricforms-grpmat-rngintelt)

  - [`AntisymmetricForms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]`](forms.md#function-antisymmetricforms-grpmat-rngintelt)

  - [`NumberOfInvariantForms(G): GrpMat → RngIntElt, RngIntElt`](forms.md#function-numberofinvariantforms-grpmat)

  - [`NumberOfSymmetricForms(G): GrpMat → RngIntElt`](forms.md#function-numberofsymmetricforms-grpmat)

  - [`NumberOfAntisymmetricForms(G): GrpMat → RngIntElt`](forms.md#function-numberofantisymmetricforms-grpmat)

- [Endomorphisms](Endomorphisms.md)

  - [`EndomorphismRing(G): GrpMat → AlgMat`](Endomorphisms.md#function-endomorphismring-grpmat)

  - [`EndomorphismAlgebra(G): GrpMat → AlgMat`](Endomorphisms.md#function-endomorphismalgebra-grpmat)

  - [`CentreOfEndomorphismRing(G): GrpMat → AlgMat`](Endomorphisms.md#function-centreofendomorphismring-grpmat)

  - [`CentreOfEndomorphismAlgebra(G): GrpMat → AlgMat`](Endomorphisms.md#function-centreofendomorphismalgebra-grpmat)

  - [`DimensionOfEndomorphismRing(G): GrpMat → RngIntElt`](Endomorphisms.md#function-dimensionofendomorphismring-grpmat)

  - [`DimensionOfCentreOfEndomorphismRing(G): GrpMat → RngIntElt`](Endomorphisms.md#function-dimensionofcentreofendomorphismring-grpmat)

  - [`Endomorphisms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]`](Endomorphisms.md#function-endomorphisms-grpmat-rngintelt)

  - [`CentralEndomorphisms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]`](Endomorphisms.md#function-centralendomorphisms-grpmat-rngintelt)

- [New Groups From Others](Others.md)

  - [`BravaisGroup(G): GrpMat[RngInt] → GrpMat`](Others.md#function-bravaisgroup-grpmat-rngint)

  - [`IntegralGroup(G): GrpMat → GrpMat, AlgMatElt`](Others.md#function-integralgroup-grpmat)

  - [`IntegralGroup(G): [Mtrx] → [Mtrx], AlgMatElt`](Others.md#function-integralgroup-mtrx)

- [Perfect Forms and Normalizers](Normalizer.md)

  - [`PerfectForms(G): GrpMat[RngInt] → SeqEnum`](Normalizer.md#function-perfectforms-grpmat-rngint)

  - [`NormalizerGLZ(G): GrpMat[RngInt] → GrpMat[RngInt]`](Normalizer.md#function-normalizerglz-grpmat-rngint)

  - [`CentralizerGLZ(G): GrpMat[RngInt] → GrpMat[RngInt]`](Normalizer.md#function-centralizerglz-grpmat-rngint)

- [Conjugacy](Conjugacy.md)

  - [`ZClasses(G): GrpMat → SeqEnum, SeqEnum`](Conjugacy.md#function-zclasses-grpmat)

  - [`IsGLZConjugate(G, H): GrpMat[RngInt], GrpMat[RngInt] → BoolElt, GrpMatElt`](Conjugacy.md#function-isglzconjugate-grpmat-rngint-grpmat-rngint)

  - [`IsBravaisEquivalent(G, H): GrpMat[RngInt], GrpMat[RngInt] → BoolElt, GrpMatElt`](Conjugacy.md#function-isbravaisequivalent-grpmat-rngint-grpmat-rngint)

  - [`IsGLQConjugate(G, H): GrpMat, GrpMat → BoolElt, GrpMatElt`](Conjugacy.md#function-isglqconjugate-grpmat-grpmat)

- [Conjugacy Tests for Matrices](Conjugacy_Matrices.md)

  - [`IsGLZConjugate(A, B): AlgMatElt, AlgMatElt → BoolElt, GrpMatElt`](Conjugacy_Matrices.md#function-isglzconjugate-algmatelt-algmatelt)

  - [`IsGLZConjugate(A, B): GrpMatElt, GrpMatElt → BoolElt, GrpMatElt`](Conjugacy_Matrices.md#function-isglzconjugate-grpmatelt-grpmatelt)

  - [`IsSLZConjugate(A, B): AlgMatElt, AlgMatElt → BoolElt, GrpMatElt`](Conjugacy_Matrices.md#function-isslzconjugate-algmatelt-algmatelt)

  - [`IsSLZConjugate(A, B): GrpMatElt, GrpMatElt → BoolElt, GrpMatElt`](Conjugacy_Matrices.md#function-isslzconjugate-grpmatelt-grpmatelt)

  - [`CentralizerGLZ(A): AlgMatElt → GrpMat`](Conjugacy_Matrices.md#function-centralizerglz-algmatelt)

  - [`CentralizerGLZ(A): GrpMatElt → GrpMat`](Conjugacy_Matrices.md#function-centralizerglz-grpmatelt)

  - [`AreGLConjugate(A, B : parameters): AlgMatElt, AlgMatElt → BoolElt, AlgMatElt`](Conjugacy_Matrices.md#function-areglconjugate-algmatelt-algmatelt)

  - [`AreGLConjugate(A, B : parameters): GrpMatElt, GrpMatElt → BoolElt, GrpMatElt`](Conjugacy_Matrices.md#function-areglconjugate-grpmatelt-grpmatelt)

  - [`GLCentraliser(A : parameters): AlgMatElt → GrpMat`](Conjugacy_Matrices.md#function-glcentraliser-algmatelt)

  - [`GLCentraliser(A : parameters): GrpMatElt → GrpMat`](Conjugacy_Matrices.md#function-glcentraliser-grpmatelt)

- [Examples](Examples.md)

  - [`Example: Z Classes`](Examples.md#example-ex-000ead)

  - [`Example: conjugacy`](Examples.md#example-ex-0cc747)

  - [`Example: Conjugacy Matrices`](Examples.md#example-ex-7ed711)

  - [`Example: GLnZClasses EHOB`](Examples.md#example-ex-2c3b15)