Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`NewLinearAlgebraPaclet`
UpperLeftTriangularize  |
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Details and Options
Examples
(1)
Basic Examples
(1)
Upper left triangularize a matrix:
In[1]:=
MatrixForm@
[18]
 | UpperLeftTriangularize |
 | PyramidMatrix |
Out[1]//MatrixForm=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 0 | 0 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8 | 8 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here's a smaller example:
In[2]:=
MatrixForm@
[5]
| UpperLeftTriangularize |
| PyramidMatrix |
Out[2]//MatrixForm=
1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 0 |
1 | 2 | 3 | 0 | 0 |
1 | 2 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
Use a different antidiagonal (this is a super antidiagonal):
In[3]:=
MatrixForm@
[5],1
| UpperLeftTriangularize |
 | PyramidMatrix |
Out[3]//MatrixForm=
1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 2 | 0 |
1 | 2 | 2 | 0 | 0 |
1 | 1 | 0 | 0 | 0 |
Use a sub antidiagonal:
In[4]:=
MatrixForm@
[5],-1
| UpperLeftTriangularize |
| PyramidMatrix |
Out[4]//MatrixForm=
1 | 1 | 1 | 1 | 0 |
1 | 2 | 2 | 0 | 0 |
1 | 2 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 |
Here is an array plot:
In[5]:=
ArrayPlot
[100]
| UpperLeftTriangularize |
| PyramidMatrix |
Out[5]=
Here's a matrix plot:
In[6]:=
MatrixPlot
[100]
| UpperLeftTriangularize |
| PyramidMatrix |
Out[6]=
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""