Basic Examples

Construct an antidiagonal matrix:
[◼]
AntidiagonalMatrix
[{a,b,c}]//MatrixForm
In[]:=
0
0
a
0
b
0
c
0
0
Out[]//MatrixForm=
A super-antidiagonal matrix:
[◼]
AntidiagonalMatrix
[{a,b},1]//MatrixForm
In[]:=
0
a
0
b
0
0
0
0
0
Out[]//MatrixForm=
A sub-antidiagonal matrix:
[◼]
AntidiagonalMatrix
[{a,b},-1]//MatrixForm
In[]:=
0
0
0
0
0
a
0
b
0
Out[]//MatrixForm=

Scope

The elements in AntidiagonalMatrix are chosen to match the elements of the vector:
v=1/Range[3];
In[]:=
Exact number entries:
[◼]
AntidiagonalMatrix
[v]//MatrixForm
In[]:=
0
0
1
0
1
2
0
1
3
0
0
Out[]//MatrixForm=
Machine-number entries:
[◼]
AntidiagonalMatrix
[N[v]]//MatrixForm
In[]:=
0.
0.
1.
0.
0.5
0.
0.333333
0.
0.
Out[]//MatrixForm=
Arbitrary-precision number entries:
[◼]
AntidiagonalMatrix
[N[v,20]]//MatrixForm
In[]:=
0
0
1.0000000000000000000
0
0.50000000000000000000
0
0.33333333333333333333
0
0
Out[]//MatrixForm=
When the vector is a
SparseArray
object,
AntidiagonalMatrix
will give a
SparseArray
object:
v=SparseArray[Range[100]]
In[]:=
SparseArray
Specified elements: 100
Dimensions: {100}

Out[]=
[◼]
AntidiagonalMatrix
[v]
In[]:=
SparseArray
Specified elements: 100
Dimensions: {100,100}

Out[]=
Pad with zeros to make a larger square matrix:
[◼]
AntidiagonalMatrix
[{1,2,3},0,5]//MatrixForm
In[]:=
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
Out[]//MatrixForm=
Make a square matrix with the specified dimension:
[◼]
AntidiagonalMatrix
[{1,2,3,4,5},0,3]//MatrixForm
In[]:=
0
0
1
0
2
0
3
0
0
Out[]//MatrixForm=
Rectangular diagonal matrices:
[◼]
AntidiagonalMatrix
[{1,2,3},0,{3,5}]//MatrixForm
In[]:=
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
Out[]//MatrixForm=
[◼]
AntidiagonalMatrix
[{1,2,3},0,{5,3}]//MatrixForm
In[]:=
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
Out[]//MatrixForm=

Applications

Express a matrix as the sum of its antidiagonal and off-antidiagonal parts:
MatrixForm[m=Array[a
##
&,{3,3}]]
In[]:=
a
1,1
a
1,2
a
1,3
a
2,1
a
2,2
a
2,3
a
3,1
a
3,2
a
3,3
Out[]//MatrixForm=
Construct a 5×5 tri-antidiagonal matrix:
Extract the antidiagonal from an antidiagonal rectangular matrix:
Reconstruct the original matrix from the antidiagonal:

Properties and Relations