The introduction to spectral analysis by B. Hofmann-Wellenhof and H. Moritz from the Institute of Theoretical Geodesy at the Technical University Graz discusses the concept of diagonal matrices in the context of linear equation systems. The authors start with a general linear equation system \( y = A x \), where \( A \) is a square matrix. They then introduce the idea of "discrete convolution," which involves multiplication followed by summation. The goal of spectral analysis is to eliminate the summation part of these convolutions. To simplify the discussion, the authors focus on diagonal matrices, which have the form \( B = \begin{bmatrix} b_1 & 0 & 0 \\ 0 & b_2 & 0 \\ 0 & 0 & b_3 \end{bmatrix} \). For a diagonal matrix, the linear equation system reduces to \( y = B x \), resulting in three separate equations: \( y_1 = b_1 x_1 \), \( y_2 = b_2 x_2 \), and \( y_3 = b_3 x_3 \). These equations are analogous to the more complex form but are simpler to handle.The introduction to spectral analysis by B. Hofmann-Wellenhof and H. Moritz from the Institute of Theoretical Geodesy at the Technical University Graz discusses the concept of diagonal matrices in the context of linear equation systems. The authors start with a general linear equation system \( y = A x \), where \( A \) is a square matrix. They then introduce the idea of "discrete convolution," which involves multiplication followed by summation. The goal of spectral analysis is to eliminate the summation part of these convolutions. To simplify the discussion, the authors focus on diagonal matrices, which have the form \( B = \begin{bmatrix} b_1 & 0 & 0 \\ 0 & b_2 & 0 \\ 0 & 0 & b_3 \end{bmatrix} \). For a diagonal matrix, the linear equation system reduces to \( y = B x \), resulting in three separate equations: \( y_1 = b_1 x_1 \), \( y_2 = b_2 x_2 \), and \( y_3 = b_3 x_3 \). These equations are analogous to the more complex form but are simpler to handle.