‣ MatrixCategory( F ) | ( attribute ) |
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.
‣ MatrixCategoryAsCategoryOfRows( 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.
‣ 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 \(d\).
‣ 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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