which are called
Now the matrix A can be considered as cellular or block matrix:
which elements are cells (blocks).
– square matrices (generally speaking, of different orders), and outside of cells zeros are. Note, that
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.
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 .
S o l u t i o n .
Contents >> Applied Mathematics >> Matrix Algebra >> Principles of Matrix Calculation >> Cellular matrices