# Name for diagonals of a matrix

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.

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

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

• do you have a (serious) reference ? I know "secondary" as the \\ diagonals next or parallel to the main diagonal.
– Max
Commented Jul 10 at 13:48
• @Max A simple image search for “secondary diagonal” yields mostly /. Commented Jul 10 at 14:39
• yes, there are a lot of web pages that say "secondary" is "/", but this is exactly my concern : I do think that that is an erroneous information that keeps spreading. Did you find serious textbooks (and I do mean serious, not by random self-declared experts) that say so?
– Max
Commented Jul 11 at 17:10
• @Max If a lot of people use the “wrong” term to mean something, and they are understood by their audience, is it really the wrong term? (See: Prescriptivism vs Descriptivism) Commented Jul 13 at 3:26
• I agree to some extend. Language/words are tools for communication, so one can consider "correct" or legitimate a "wrong" word that is "correctly" understood (as for "whole" numbers which many understand as nonnegative integers, which doesn't make sense - "whole" means just the exact same as "integer" or "entier" in French or "ganz" in German). I don't think that popularity or current use is a criterium for right or wrong in science. Misnomers cause confusion. Are you not worried that the class of birds is a subgroup of the order of dinosaurs in the class of reptiles?
– Max
Commented Jul 16 at 3:52

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.

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.