Explain Block Multiplication to Me

[bodensee9]

Can someone explain "block multiplication" to me? It's not in the book, except in the context of a question as follows:

So the rule is that Matrix [A B] * colum matrix [C D] = [AC+BD] And I am supposed to verify it. but can I just ask how I would go about doing that since I really don't know what block multiplication does or what I'm supposed to multiply? Thanks.

 

[AlephZero]

"Block multiplication" means that in your example A B C and D are matrices, not scalars. The dimensions of A B C and D must be compatible with each other, so the matrix expression AC + BD is defined. The row dimension of A is the same as the column dimension of C, etc.

Verify it by showing it gives the same answer as the standard definition of matrix multiplication. Write A as an array of scalars $a_{ij}$ and so on.