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Mathematica > Mathematics and Algorithms > Matrices and Linear Algebra > Constructing Matrices > ToeplitzMatrix >

Mathematica > Mathematics and Algorithms > Graphs & Networks > Graph Programming > Matrices and Linear Algebra > Constructing Matrices > ToeplitzMatrix >

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BUILT-IN MATHEMATICA SYMBOL

ToeplitzMatrix

ToeplitzMatrix[n]
gives the n×n Toeplitz matrix with first row and first column being successive integers.

ToeplitzMatrix

gives the Toeplitz matrix whose first column consists of elements

, ....

ToeplitzMatrix

gives the Toeplitz matrix with elements

down the first column, and

across the first row.

MORE INFORMATION

The element must be the same as . »

EXAMPLES

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Basic Examples (3)

4×4 Toeplitz matrix:

Toeplitz matrix with first column

and first row

4×4 Toeplitz matrix:

In[1]:=

Out[1]//MatrixForm=

In[1]:=

Out[1]//MatrixForm=

Toeplitz matrix with first column

and first row

In[1]:=

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:

Properties & Relations (4)

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:

Possible Issues (1)

When

is not the same as

, the value of

is used and

ignored:

Neat Examples (1)