Introduction

Toeplitz matrices are ubiquitous in the CMB data analysis as they describe correlation properties of stationary time-domain processes (usually instrumental noise). The matrices relevant are therefore symmetric and non-negative definite. They are also band-diagonal as the noise correlation length, i.e., the band-width in the parlance of Toeplitz algebra, is typically much shorter than length of the data. A useful and important generalization of those include :

• symmetric, block-diagonal Toeplitz matrices - describing piece-wise stationary processes, each of the blocks is in turn a symmetric, band-diagonal matrix, which can be different for the different blocks.