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1 Category of Matrices
 1.1 Constructors
 1.2 GAP Categories
 1.3 Attributes

1 Category of Matrices

1.1 Constructors

1.1-1 MatrixCategory
‣ 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.

1.1-2 VectorSpaceMorphism
‣ 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.

1.1-3 VectorSpaceObject
‣ 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.

1.2 GAP Categories

1.2-1 IsVectorSpaceMorphism
‣ IsVectorSpaceMorphism( object )( filter )

Returns: true or false

The GAP category of morphisms in the category of matrices of a field F.

1.2-2 IsVectorSpaceObject
‣ IsVectorSpaceObject( object )( filter )

Returns: true or false

The GAP category of objects in the category of matrices of a field F.

1.3 Attributes

1.3-1 UnderlyingFieldForHomalg
‣ 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.

1.3-2 UnderlyingMatrix
‣ UnderlyingMatrix( alpha )( attribute )

Returns: a homalg matrix

The argument is a morphism \alpha in a matrix category. The output is its underlying matrix M.

1.3-3 UnderlyingFieldForHomalg
‣ 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.

1.3-4 Dimension
‣ 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.

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