‣ MatrixCategory( F ) | ( operation ) |
Returns: a category
The argument is a homalg field F. The output is the matrix category over F. Objects in this category are non-negative integers. Morphisms from a non-negative integer m to a non-negative integer n are given by m \times n matrices.
‣ VectorSpaceMorphism( S, M, R ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(S,R)
The arguments are an object S in the category of matrices over a homalg field F, a homalg matrix M over F, and another object R in the category of matrices over F. The output is the morphism S \rightarrow R in the category of matrices over F whose underlying matrix is given by M.
‣ VectorSpaceObject( d, F ) | ( operation ) |
Returns: an object
The arguments are a non-negative integer d and a homalg field F. The output is an object in the category of matrices over F of dimension d. This function delegates to MatrixCategoryObject.
‣ MatrixCategoryObject( cat, d ) | ( operation ) |
Returns: an object
The arguments are a matrix category cat over a field and a non-negative integer d. The output is an object in cat of dimension d.
‣ MatrixCategory_as_CategoryOfRows( F ) | ( operation ) |
Returns: a category
The argument is a homalg field F. The output is the matrix category over F, constructed internally as a wrapper category of the CategoryOfRows of F. Only available if the package FreydCategoriesForCAP is available.
‣ UnderlyingFieldForHomalg( alpha ) | ( attribute ) |
Returns: a homalg field
The argument is a morphism \alpha in the matrix category over a homalg field F. The output is the field F.
‣ UnderlyingMatrix( alpha ) | ( attribute ) |
Returns: a homalg matrix
The argument is a morphism \alpha in a matrix category. The output is its underlying matrix M.
‣ UnderlyingFieldForHomalg( A ) | ( attribute ) |
Returns: a homalg field
The argument is an object A in the matrix category over a homalg field F. The output is the field F.
‣ Dimension( A ) | ( attribute ) |
Returns: a non-negative integer
The argument is an object A in a matrix category. The output is the dimension of A.
‣ IsVectorSpaceMorphism( object ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in the category of matrices of a field F.
‣ IsVectorSpaceObject( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in the category of matrices of a field F.
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