if , then

Note the change in order of and (we have instead of ). Similarly, if , then should be replaced with (i.e. we get ) and if , then we should have . Note for the last two results, you have to use commutativity of the underlying ring, but not for the first two.

This formula has been generalized to matrices composed of more than blocks, again under appropriate commutativity conditions among the individual blocks.

For and , the following formula holds (even if and do not commute)

Special types of block matrices

1.Previous
3.Next