Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`NewLinearAlgebraPaclet`
PyramidMatrix  |
|
| | ||||
Details and Options
Examples
(2)
Basic Examples
(1)
Here are some pyramid matrices:
In[1]:=
MatrixForm/@
/@Range[7]
 | PyramidMatrix |
Out[1]=
(
),
,
,
,
,
,
1 |
1 | 1 |
1 | 1 |
1 | 1 | 1 |
1 | 2 | 1 |
1 | 1 | 1 |
1 | 1 | 1 | 1 |
1 | 2 | 2 | 1 |
1 | 2 | 2 | 1 |
1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
Here is a big pyramid matrix with an even number of elements. Notice the 4 12s in the middle:
In[2]:=
| PyramidMatrix |
Out[2]//MatrixForm=
1 | 1 | 1 | 1 | 1 | 1 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 10 | 10 | 10 | 10 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 11 | 11 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 11 | 11 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 10 | 10 | 10 | 10 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Here is a big pyramid matrix with an odd number of elements. Notice the 13 in the middle of the ring of 12s:
In[3]:=
| PyramidMatrix |
Out[3]//MatrixForm=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 11 | 11 | 11 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 12 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 12 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 11 | 11 | 11 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Format the matrix with a dataset:
In[4]:=
| PyramidMatrix |
Out[4]=
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 |
Format the matrix with a grid:
In[5]:=
Grid
[9]
| PyramidMatrix |
Out[5]=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Format the matrix with a frame too.:
In[6]:=
Grid
[9],FrameTrue
 | PyramidMatrix |
Out[6]=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Use different frame options. Put a grid around all elements:
In[7]:=
Grid
[9],FrameAll
| PyramidMatrix |
Out[7]=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Make a table instead:
In[8]:=
TableForm
[9]
| PyramidMatrix |
Out[8]//TableForm=
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 5 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 4 | 4 | 4 | 3 | 2 | 1 |
1 | 2 | 3 | 3 | 3 | 3 | 3 | 2 | 1 |
1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Make a table view instead:
In[9]:=
TableView
[9]
| PyramidMatrix |
Out[9]=
Make an array plot:
In[10]:=
ArrayPlot
[9]
| PyramidMatrix |
Out[10]=
Make an array plot with different colors:
Make an image.
There might be a way to make a 3D image somehow.