Block Toeplitz Matrices provides a tutorial introduction and in-depth expose of this important mathematical technique used in Communications, Information Theory, and Signal Processing. The matrix representations of discrete-time causal finite impulse response (FIR), multiple-input multiple-output (MIMO) filters, and correlation matrices of vector wide sense stationary (WSS) processes are all block Toeplitz.

The monograph deals with the asymptotic behaviour of eigenvalues, products and inverses of block Toeplitz matrices, with the concept of asymptotically equivalent sequences of matrices being the key concept. However, since the blocks of block Toeplitz matrices are, in general, not square, the definition of asymptotically equivalent sequences of matrices are extended to sequences of non-square matrices.

Furthermore, the monograph covers any function of block Toeplitz matrices and considers block Toeplitz matrices generated by the Fourier coefficients of any continuous matrix-valued function. Block Toeplitz Matrices is an advanced level tutorial on a mathematical technique with applications in many engineering disciplines.