Toeplitz matrix
In the mathematical discipline of linear algebra, a Toeplitz matrix, named after Otto Toeplitz, or diagonal constant matrix is a special kind of computer science because it can be shown that the addition of two Toeplitz matrices can be done in O(n) time and the matrix multiplication of two Toeplitz matrices can be done in O(n log n) time. Toeplitz systems of form <math>Ax=b<math> can be solved by Levinson recursion.
They are also closely connected with Fourier series, because the multiplication operator by a trigonometric polynomial, compressed to a finite-dimensional space, can be represented by such a matrix.
If a Toeplitz matrix has the additional property that <math>a_i=a_{i+n}<math>, then it is a circulant matrix.
