Linear Algebra/Partitioned Matrices

A partitioned matrix also called a block matrix is a partition of a matrix into rectangular smaller matrices called blocks.

The matrix $$P$$ can be partitioned into 4 2×2 blocks
 * $$P = \begin{bmatrix}

1 & 1 & 2 & 2\\ 1 & 1 & 2 & 2\\ 3 & 3 & 4 & 4\\ 3 & 3 & 4 & 4\end{bmatrix}$$


 * $$P_{11} = \begin{bmatrix}

1 & 1 \\ 1 & 1 \end{bmatrix},  P_{12} = \begin{bmatrix} 2 & 2\\ 2 & 2\end{bmatrix}, P_{21} = \begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix},  P_{22} = \begin{bmatrix} 4 & 4\\ 4 & 4\end{bmatrix}$$

Then we can write the partitioned matrix like this
 * $$P_{\text{partitioned}} = \begin{bmatrix}

P_{11} & P_{12} \\ P_{21} & P_{22} \end{bmatrix}$$