THE HEIGHT CHARACTERISTIC OF BLOCK TRIANGULAR MATRICES

It is shown that the height characteristic of a block triangular matri x. A with square diagonal blocks majorizes the dual of the sequence of differences of maximal cardinalities of singular k-paths in a certain graph, which is determined by the height characteristics of the diago nal blocks and the reduced graph of A. It is also shown that an equali ty holds in the generic case. This result implies previously known res ults for the block triangular case as well as for the triangular case. It also yields the Index Theorem for the general case, with an equali ty in the generic case.