## Encyclopedia > Toeplitz matrix

Article Content

# Toeplitz matrix

In linear algebra, a Toeplitz matrix is a square matrix with constant (negative sloping) diagonals, i.e;

$\begin{bmatrix} a & b & c & d & e \\ f & a & b & c & d \\ g & f & a & b & c \\ h & g & f & a & b \\ j & h & g & f & a \\ \end{bmatrix}$

In mathematical terms:

$a_{i,j} = a_{i-1,j-1}$

These matrices is useful in computer science because it can be shown that the addition of two Toeplitz matricies can be done in O(n) time and the matrix multiplication of two Toepliz matrices can be done in O(nlogn) time.

The matrix is named after Otto Toeplitz[?] (1881-1940), a German mathematician.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 List of rare diseases starting with A ... Aarskog Ose Pande syndrome[?] Aarskog syndrome[?] Aase Smith syndrome[?] Aase syndrome[?] ABCD syndrome[?] Abdallat Davis Farrage syndrome[?] Abdominal aortic ...