Hankel matrix

Occupation pattern of a Hankel matrix of size 5 × 5

A Hankel matrix , named after Hermann Hankel (1839–1873), describes a square matrix in which only one constant value occurs on each counter-diagonal running from top right to bottom left . It is completely described by the top row and the rightmost column of the matrix.

A Hankel matrix is ​​a symmetrical matrix . The dimension of the vector space of the Hankel matrices is . ${\displaystyle n\times n}$ ${\displaystyle 2n-1}$

As with the related Toeplitz matrices, this simplification allows the use of particularly efficient methods for matrix operations such as multiplication and inversion .

example

Here is an example of a -Hankel matrix: ${\displaystyle 4\times 4}$

${\displaystyle M={\begin{pmatrix}1&2&3&4\\2&3&4&5\\3&4&5&6\\4&5&6&7\\\end{pmatrix}}}$

Individual evidence

1. ^ Hankel matrix . In: Guido Walz (Ed.): Lexicon of Mathematics . 1st edition. Spektrum Akademischer Verlag, Mannheim / Heidelberg 2000, ISBN 3-8274-0439-8 ( google.de ).