1+ #
2+ gap> empty_0x2 := NewZeroMatrix(IsPlistMatrixRep, Integers, 0 , 2 );
3+ < 0x2 - matrix over Integers>
4+ gap> empty_2x0 := NewZeroMatrix(IsPlistMatrixRep, Integers, 2 , 0 );
5+ < 2x0- matrix over Integers>
6+ gap> empty_0x0 := NewZeroMatrix(IsPlistMatrixRep, Integers, 0 , 0 );
7+ < 0x0 - matrix over Integers>
8+ gap> IsEmptyMatrix(empty_0x2);
9+ true
10+ gap> IsEmptyMatrix(empty_2x0);
11+ true
12+ gap> IsEmptyMatrix(empty_0x0);
13+ true
14+
115#
216gap> IsGeneralizedCartanMatrix(NullMat(3 , 3 ));
317false
@@ -21,6 +35,12 @@ gap> IsGeneralizedCartanMatrix([[2,-2],[-2,2]]);
2135true
2236
2337#
38+ gap> IsDiagonalMat(empty_0x2);
39+ true
40+ gap> IsDiagonalMat(empty_2x0);
41+ true
42+ gap> IsDiagonalMat(empty_0x0);
43+ true
2444gap> IsDiagonalMat(NullMat(3 , 3 ));
2545true
2646gap> IsDiagonalMat(NullMat(1 , 3 ));
@@ -45,6 +65,12 @@ gap> IsDiagonalMat([[1,0,0],[0,1,0]]);
4565true
4666
4767#
68+ gap> IsUpperTriangularMat(empty_0x2);
69+ true
70+ gap> IsUpperTriangularMat(empty_2x0);
71+ true
72+ gap> IsUpperTriangularMat(empty_0x0);
73+ true
4874gap> IsUpperTriangularMat(NullMat(3 , 3 ));
4975true
5076gap> IsUpperTriangularMat(NullMat(1 , 3 ));
@@ -67,6 +93,12 @@ gap> IsUpperTriangularMat([[1,1,1],[0,1,1]]);
6793true
6894
6995#
96+ gap> IsLowerTriangularMat(empty_0x2);
97+ true
98+ gap> IsLowerTriangularMat(empty_2x0);
99+ true
100+ gap> IsLowerTriangularMat(empty_0x0);
101+ true
70102gap> IsLowerTriangularMat(NullMat(3 , 3 ));
71103true
72104gap> IsLowerTriangularMat(NullMat(1 , 3 ));
@@ -89,6 +121,12 @@ gap> IsLowerTriangularMat([[1,0],[1,1],[1,1]]);
89121true
90122
91123#
124+ gap> IsSquareMat(empty_0x2);
125+ false
126+ gap> IsSquareMat(empty_2x0);
127+ false
128+ gap> IsSquareMat(empty_0x0);
129+ true
92130gap> IsSquareMat(NullMat(3 , 3 ));
93131true
94132gap> IsSquareMat(IdentityMat(3 ));
@@ -105,6 +143,12 @@ gap> IsSquareMat([[1,2,3],[4,5,6]]);
105143false
106144
107145#
146+ gap> IsSymmetricMat(empty_0x2);
147+ false
148+ gap> IsSymmetricMat(empty_2x0);
149+ false
150+ gap> IsSymmetricMat(empty_0x0);
151+ true
108152gap> IsSymmetricMat(NullMat(3 , 3 ));
109153true
110154gap> IsSymmetricMat(IdentityMat(3 ));
@@ -129,6 +173,12 @@ gap> IsSymmetricMat([[1,2],[3,4],[5,6]]);
129173false
130174
131175#
176+ gap> IsAntisymmetricMat(empty_0x2);
177+ false
178+ gap> IsAntisymmetricMat(empty_2x0);
179+ false
180+ gap> IsAntisymmetricMat(empty_0x0);
181+ true
132182gap> IsAntisymmetricMat(NullMat(3 , 3 ));
133183true
134184gap> IsAntisymmetricMat([[ 0 ]] );
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