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I am looking for the terms to use for particular types of diagonals in two dimensional matrices. I have heard the longest diagonal, from top-left element and in the direction down-right often called the "leading diagonal".

-What about the 'other' diagonal, from the top right going down-left? Does it have a common name?

-Any general name to use for any diagonal going top-left to bottom-right direction, not necessarily just the longest one(s)? I am searching for a term to distinguish between these types of diagonals and the ones in the 'other' direction. Preferably the term should not be restricted to square matrices.

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$\diagdown$ Major, Principal, Primary, Main; diagonal $\diagdown$

$\diagup$ Minor, Counter, Secondary, Anti-; diagonal $\diagup$

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The diagonal from the top left corner to the bottom right corner of a square matrix is called the main diagonal or leading diagonal.

The other diagonal from the top right to the bottom left corner is called antidiagonal or counterdiagonal.

You can also define the main diagonal and antidiagonal of a rectangular matrix. See here for more.

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The general term for any diagonal going top-left to bottom-right direction is $k$-diagonal where $k$ is an offset form the main diagonal.

$k=1$ is the superdiagonal, $k=0$ is the main diagonal, and $k=-1$ is the subdiagonal.

According to Mathworld, the general term for the antidiagonals seems to be skew-diagonals.

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