# Matrix algebra

1. Apr 28, 2005

### el_hijoeputa

Some big matrix, like 4x4 ones, can be written as groups of 2x2 matrices.

For example,
$$H = \left(\begin{array}{cccc}1 & 0 & 1 & 0\\0 & 1 & 0 & 1\\1 & 0 & 1 & 0\\0 & 1 & 0 & 1\end{array}\right) = \left(\begin{array}{cc}1 & 1\\1 & 1\end{array}\right)$$
where the 1 in the last matrix represents a 2x2 identity matrix.

I just want to know how to deal with this algebra the right way, and fast.
If A, B, C, D, W, X, Y, and Z are 2x2 matrices.

$$\left(\begin{array}{cc}A & B\\C & D\end{array}\right) \left(\begin{array}{cc}W & X\\Y & Z\end{array}\right) = \left(\begin{array}{cc}(AW+BY) & (AX+BZ)\\(CW+DY) & (CX+DZ)\end{array}\right)$$

Is this right?

2. Apr 28, 2005