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Principle Submatrices

Given an n × n matrix M = (mi, j), the principle submatrices are M1, M2, M3, ..., Mn where Mk is an k × k matrix, the (i, j)th entry equals the (i, j)th entry of M. Two are striaght-forward: M1 = (m1, 1) and Mn = M.

For example, the four principle submatrices of the matrix