Package dk.jonaslindstrom.ruffini.common.matrices.structures

Class GeneralLinearGroup<E,F extends Field<E>>

java.lang.Object
dk.jonaslindstrom.ruffini.common.matrices.structures.GeneralLinearGroup<E,F>
Type Parameters:
E - Element type.
F - Field type.
All Implemented Interfaces:
Group<Matrix<E>>, Monoid<Matrix<E>>, Semigroup<Matrix<E>>, Set<Matrix<E>>
public class GeneralLinearGroup<E,F extends Field<E>> extends Object implements Group<Matrix<E>>
This class represents the general linear group GL(n, F) of invertible n × n matrices over a field F.

  • Constructor Details

    • GeneralLinearGroup

      public GeneralLinearGroup(F field, int n)

  • Method Details

    • invert

      public Matrix<E> invert(Matrix<E> a)
      Description copied from interface: Group
      Return the inverse a-1.
      Specified by:
      invert in interface Group<E>

    • identity

      public Matrix<E> identity()
      Description copied from interface: Monoid
      Return the identity element of this monoid.
      Specified by:
      identity in interface Monoid<E>

    • multiply

      public Matrix<E> multiply(Matrix<E> a, Matrix<E> b)
      Description copied from interface: Semigroup
      Return the result of the product ab in this group.
      Specified by:
      multiply in interface Semigroup<E>

    • toString

      public String toString(Matrix<E> a)
      Description copied from interface: Set
      Returns a human-readable string representation of an element in this set.
      Specified by:
      toString in interface Set<E>

    • equals

      public boolean equals(Matrix<E> a, Matrix<E> b)
      Description copied from interface: Set
      Returns true if and only if a = b as elements of this set.
      Specified by:
      equals in interface Set<E>

    • toString

      public String toString()
      Overrides:
      toString in class Object