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 Matrix Algebra - Cellular matrices Cellular matrices Let's consider some matrix A and we’ll split it into matrices of lower order: which are called cells or blocks . Here cells (blocks) are matrices: Now the matrix A can be considered as cellular or block matrix: which elements are cells (blocks). Apparently, that splitting of any matrix into cells (blocks) is maybe executed by various ways. In that specific case the cellular matrix can be quasi-diagonal one: where cells – square matrices (generally speaking, of different orders), and outside of cells zeros are. Note, that Cellular matrices of the same dimensions and with identical splitting are called conform . Operations with cellular matrices are carried out by the same rules, as with usual matrices. 1. Addition and subtraction of cellular matrices Let there are two conform cellular matrices: where p = r , q = s and cells of identical dimension. Then Subtraction of cellular matrices is carried out similarly. 2. Multiplication of cellular matrices Multiplication of a cellular matrix to a number (scalar) Let A – a cellular matrix and h – a number, then we have: Multiplication of cellular matrices Let's consider two conform cellular matrices: and q = r . Let all cells such, that a number of columns of a cell is equal to a number of rows of a cell (For example, apparently, that it takes place in that specific case, when all cells – square matrices and have also the same order). Then it is easy to show, that a product of matrices A and B is too a cellular matrix: where that is multiplication of cellular matrices is similar to multiplication of numerical matrices . E x a m p l e .  Multiply the cellular matrices S o l u t i o n . < Previous Contents Next >