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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 $JāŠ‚{1,2,..,n}$, 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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    http://idioms.yourdictionary.com/any-old – 2012-09-30