# Names for special submatrices?

Let $(a_{ij}), i,j \in \{1,...,n\}$ be a matrix. What are the names for the following special square submatrices:

• for any set of indices $J⊂{1,2,..,n}$, the submatrix $(a_{jk})j,k\in J$,
• a submatrix formed by removing the last m rows and last m columns;
• a submatrix formed by removing any m rows and any m columns.

Does a principal submatrice mean any of the above three kinds? Thanks!

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The first kind is a principal submatrix, the second kind is a leading principal submatrix, and the last kind is just any old submatrix. :-)

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Thanks! Why do you call the last one "old"? –  Tim Sep 30 '12 at 18:49
It's just an idiom, not a mathematical definition. –  Hans Lundmark Sep 30 '12 at 18:49