Block Matrix - Block Toeplitz Matrices

Block Toeplitz Matrices

A block Toeplitz matrix is another special block matrix, which contains blocks that are repeated down the diagonals of the matrix, as a Toeplitz matrix has elements repeated down the diagonal.

A block Toeplitz matrix A has the form

\mathbf{A} = \begin{bmatrix} \mathbf{A}_{(1,1)} & \mathbf{A}_{(1,2)} & & & \cdots & \mathbf{A}_{(1,n-1)} & \mathbf{A}_{(1,n)} \\ \mathbf{A}_{(2,1)} & \mathbf{A}_{(1,1)} & \mathbf{A}_{(1,2)} & & & & \mathbf{A}_{(1,n-1)} \\ & \ddots & \ddots & \ddots & & & \vdots \\ & & \mathbf{A}_{(2,1)} & \mathbf{A}_{(1,1)} & \mathbf{A}_{(1,2)} & & \\ \vdots & & & \ddots & \ddots & \ddots & \\ \mathbf{A}_{(n-1,1)} & & & & \mathbf{A}_{(2,1)} & \mathbf{A}_{(1,1)} & \mathbf{A}_{(1,2)} \\ \mathbf{A}_{(n,1)} & \mathbf{A}_{(n-1,1)} & \cdots & & & \mathbf{A}_{(2,1)} & \mathbf{A}_{(1,1)} \end{bmatrix}.

Read more about this topic:  Block Matrix

Famous quotes containing the word block:

    “Dug from the tomb of taste-refining time,
    Each form is exquisite, each block sublime.
    Or good, or bad,—disfigur’d, or deprav’d,—
    All art, is at its resurrection sav’d;
    All crown’d with glory in the critic’s heav’n,
    Each merit magnified, each fault forgiven.”
    —Martin Archer, Sir Shee (1769–1850)