Given the interpretation "via" linear mappings and direct sums, there is a special type of block matrix that occurs for square matrices (the case "m" = "n"). For those we can assume an interpretation as an endomorphism of an "n"-dimensional space "V"; the block structure in which the bunching of rows and columns is the same is of importance because it corresponds to having a single direct sum decomposition on "V" (rather than two). In that case, for example, the diagonal blocks in the obvious sense are all square. This type of structure is required to describe the Jordan normal form.