Macaulay2 » Documentation
Packages » Kronecker :: Kronecker
next | previous | forward | backward | up | index | toc

Kronecker -- Kronecker and rational normal forms

Description

This package provides methods for computing the Kronecker and rational normal forms of a matrix.

Author

Version

This documentation describes version 0.3.3 of Kronecker, released July 16, 2010.

Citation

If you have used this package in your research, please cite it as follows:

@misc{KroneckerSource,
  title = {{Kronecker: Kronecker and rational normal forms. Version~0.3.3}},
  author = {Edward Carter},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
  • Methods
    • decomposeGradedModule(GradedModuleMap,GradedModuleMap) -- see decomposeGradedModule -- decompose a graded module over a ring of graded module maps
    • decomposeModule(Module) -- see decomposeModule -- decompose a module into a direct sum of simple modules
    • doubleDualMap(Module,Module) (missing documentation)
    • kroneckerIndices(Matrix,RingElement,RingElement) -- see kroneckerIndices -- data which classify a matrix pencil up to strict equivalence
    • kroneckerIndices(Matrix,Matrix) -- data classifying the normal form of a pair of matrices
    • kroneckerNormalForm(Matrix) -- see kroneckerNormalForm -- Kronecker normal form of a matrix of linear forms
    • kroneckerNormalForm(Matrix,RingElement,RingElement) -- see kroneckerNormalForm -- Kronecker normal form of a matrix of linear forms
    • kroneckerNormalForm(Matrix,Matrix) -- normal form of a pair of matrices of scalars
    • rationalNormalForm(Matrix) -- see rationalNormalForm -- rational normal form of a matrix

For the programmer

The object Kronecker is a package, defined in Kronecker.m2.

The source of this document is in Kronecker.m2:1053:0.