This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ToeplitzMatrix

 ToeplitzMatrix[n] gives the n×n Toeplitz matrix with first row and first column being successive integers. ToeplitzMatrixgives the Toeplitz matrix whose first column consists of elements , , .... ToeplitzMatrixgives the Toeplitz matrix with elements down the first column, and across the first row.
• The element must be the same as . »
4×4 Toeplitz matrix:
Toeplitz matrix with first column and first row :
4×4 Toeplitz matrix:
 Out[1]//MatrixForm=

 Out[1]//MatrixForm=

Toeplitz matrix with first column and first row :
 Out[1]//MatrixForm=
 Scope   (5)
Machine-number Toeplitz matrix:
20-digit-precision Toeplitz matrix:
Toeplitz matrices with complex entries:
Nonsquare Toeplitz matrices:
A common symbolic notation for Toeplitz matrices:
Size-20 Toeplitz matrix:
ToeplitzMatrix is Hermitian if is real:
has all real eigenvalues:
is diagonalizable by a unitary matrix:
ToeplitzMatrix is a circulant matrix when r=RotateRight[Reverse[c]]:
The eigenvalues can be found from:
where is the Fourier matrix and is DiagonalMatrix[v]:
HankelMatrix and ToeplitzMatrix are related by reversed identity matrix:
When is not the same as , the value of is used and ignored:
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