Example

The figure shows a product of a Toeplitz block matrix with a number of columns and rows to be excised by a data matrix. The excised columns (and rows) are marked by the dashed grids and correspond to the grayish areas of the input and output data matrices. These grayish sets of rows will be set to zero in the final result. We note that two of the three excised intervals, hereafter called gaps, of columns are broad enough that they effectively lead only to change of the size of the Toeplitz blocks including splitting one of them into two smaller ones. The third (rightmost) gap however destroys the Toeplitz structure of the second block. Indeed the effective matrix, by which white shaded part of the data matrix are multiplied by, corresponds to only dark blue areas, and does not have a Toeplitz block structure.