the 3×4 matrix presented below is divided by horizontal and vertical lines into four blocks: the top-left 2×3 block, the top-right 2×1 block, the bottom-left 1×3 block, and the bottom-right 1×1 block.

Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.

This notion can be made more precise for an by matrix by partitioning into a collection , and then partitioning into a collection . The original matrix is then considered as

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