‣ IsEmptyMatrix ( arg ) | ( filter ) |
Returns: true
or false
Category for empty matrices
‣ MakeEmptyMatrix ( m, n, R ) | ( operation ) |
Returns: IsEmptyMatrix
(5.1-1)
Create an empty m by n matrix over the ring R. The arguments m and n are nonnegative integers, and at least one of them must be zero.
‣ RingOfEmptyMatrix ( M ) | ( attribute ) |
Returns: IsRing
(Reference: IsRing)
Returns the base ring of the empty matrix M.
‣ MakeZeroMatrix ( m, n, R ) | ( operation ) |
Returns: IsEmptyMatrix
(5.1-1)
Create an m by n zero matrix over the ring R. The arguments m and n are nonnegative integers. If at least one of them is zero, then an empty matrix is constructed. Otherwise, a normal GAP matrix filled with zeros is constructed, as by NullMat
(Reference: NullMat).
gap> M := MakeEmptyMatrix( 0, 3, Rationals ); <empty 0x3 matrix over Rationals> gap> M * [ 5, 8, 2 ]; [ ] gap> [] * M; [ 0, 0, 0 ] gap> N := MakeEmptyMatrix( 3, 0, Rationals ); <empty 3x0 matrix over Rationals> gap> N * []; [ 0, 0, 0 ] gap> [ 4, 3, 7 ] * N; [ ] gap> M * N; <empty 0x0 matrix over Rationals> gap> N * M; [ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ] gap> P := MakeZeroMatrix( 2, 3, Rationals ); [ [ 0, 0, 0 ], [ 0, 0, 0 ] ] gap> P * N; <empty 2x0 matrix over Rationals> gap> N + N; <empty 3x0 matrix over Rationals> gap> N + N = N; true
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