# Is there a term for the “opposite” location in a matrix?

I'm just looking for the correct term to describe a concept:

Suppose I have a 5x5 matrix:

A B C D E
F G H I J
K L M N O
P Q R S T
U V W X Y


I can pick any two cells, let's say the cells I and Q, and observe that if I follow the row and column until they "collide," I get two more cells that form the corners of a submatrix. In other words, cells G and S are significant because they are on the same row/column of I and Q.

My question is this: Is there a term for the relationship between G and S in this situation? Anitpodes? Contras? Sisters?

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G and S are the first and last entries in the main diagonal of the submatrix determined by I and Q. –  Arturo Magidin Apr 3 '12 at 16:24
I don't see anything better than "corners"... on that note, your description as written is fine; no need for anything fancier, really. –  Guess who it is. Apr 3 '12 at 16:34
You're lucky you didn't run out of letters there. –  Bruno Joyal Apr 4 '12 at 1:55
@Bruno There's a reason the example is 5x5 :) –  jthurman Apr 4 '12 at 3:11

Following up on the comment by Arturo Magidin

G and S are the first and last entries in the main diagonal of the submatrix determined by I and Q

I'll point out that (i) two selected entries should not be in the same row or same column; (ii) if the entries K and R are picked instead, then the corresponding pair N, P is on the secondary diagonal of the submatrix. All in all, I would say something like

the entries of $2\times 2$ submatrix containing I and Q, other than I and Q.

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