Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`NewLinearAlgebraPaclet`
LowerRightTriangularMatrixQ |
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Details and Options
Examples
(1)
Basic Examples
(1)
Here a few examples.
A matrix:
In[1]:=
MatrixFormmatrix=
[12]
 | PyramidMatrix |
Out[1]//MatrixForm=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
In[2]:=
MatrixFormlowerRightTriangularMatrix=
[matrix]
| LowerRightTriangularize |
Out[2]//MatrixForm=
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 3 | 2 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 4 | 3 | 2 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 6 | 5 | 4 | 3 | 2 | 1 |
0 | 0 | 0 | 0 | 0 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
0 | 0 | 0 | 0 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
0 | 0 | 0 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
0 | 0 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
In[3]:=
| LowerRightTriangularMatrixQ |
Out[3]=
True
Here's an example that is False:
In[4]:=
MatrixForm@
[9]
| UlamMatrix |
Out[4]//MatrixForm=
65 | 64 | 63 | 62 | 61 | 60 | 59 | 58 | 57 |
66 | 37 | 36 | 35 | 34 | 33 | 32 | 31 | 56 |
67 | 38 | 17 | 16 | 15 | 14 | 13 | 30 | 55 |
68 | 39 | 18 | 5 | 4 | 3 | 12 | 29 | 54 |
69 | 40 | 19 | 6 | 1 | 2 | 11 | 28 | 53 |
70 | 41 | 20 | 7 | 8 | 9 | 10 | 27 | 52 |
71 | 42 | 21 | 22 | 23 | 24 | 25 | 26 | 51 |
72 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 |
In[5]:=
| LowerRightTriangularMatrixQ |
65 | 64 | 63 | 62 | 61 | 60 | 59 | 58 | 57 |
66 | 37 | 36 | 35 | 34 | 33 | 32 | 31 | 56 |
67 | 38 | 17 | 16 | 15 | 14 | 13 | 30 | 55 |
68 | 39 | 18 | 5 | 4 | 3 | 12 | 29 | 54 |
69 | 40 | 19 | 6 | 1 | 2 | 11 | 28 | 53 |
70 | 41 | 20 | 7 | 8 | 9 | 10 | 27 | 52 |
71 | 42 | 21 | 22 | 23 | 24 | 25 | 26 | 51 |
72 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 |
Out[5]=
False
 |
|
""