Manuals/calci/TOEPLITZ

MATRIX("TOEPLITZ",order)


  • is the size of the Toeplitz matrix.

Description

  • This function gives the matrix of order 3 with the property of toeplitz matrix.
  • A Toeplitz matrix is a matrix with the constant values along negative sloping diagonals(descending diagonal from left to right).
  • If the i,j element of A is denoted  , then we have

 .

  • Any nxn matrix A of the form:

 

  • The property of Toeplitz matrix is :Toeplitz matrices are persymmetric.
  • Symmetric Toeplitz matrices are both centrosymmetric and bisymmetric.
  • Toeplitz matrices commute asymptotically.

Examples

  • MATRIX("toeplitz",15,1..10)


A = \begin{bmatrix}

 a_{0} & a_{-1} & a_{-2} & \ldots & \ldots  &a_{-n+1}  \\
 a_{1} & a_0  & a_{-1} &  \ddots   &  &  \vdots \\
 a_{2}    & a_{1} & \ddots  & \ddots & \ddots& \vdots \\ 
\vdots &  \ddots & \ddots &   \ddots  & a_{-1} & a_{-2}\\
\vdots &         & \ddots & a_{1} & a_{0}&  a_{-1} \\

a_{n-1} & \ldots & \ldots & a_{2} & a_{1} & a_{0} \end{bmatrix}