## Encyclopedia > Toeplitz matrix

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# 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.

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