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Given a quadratic matrix $A=\begin{pmatrix} a_{11}& a_{12} &...& a_{1n}\\ a_{21} &a_{22} & ... & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & ... & a_{nn}\end{pmatrix}$, the set $\{a_{i,j}: i-j=0\}$ is called the diagonal. What do you call the set $\{a_{i,j}: i-j=k\}$ for a fixed $k$?

In German, there is the name "Nebendiagonale" (see e.g. https://de.wikipedia.org/wiki/Nebendiagonale). I am also familiar with speaking of the "erste (first) Nebendiagonale", "zweite (second) Nebendiagonale" etc. for the first or second "diagonal" below/above the main diagonal, when it is clear that we are talking about upper/lower triangular matrices. Google was no help to me.

Could you tell me the Englisch term?

Thank you!

user546191
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    I've heard "superdiagonal" used for when $i-j = -1$, and "subdiagonal" for when $i - j = 1$. – John Hughes Mar 27 '18 at 12:38
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    Look up "Haupdiagonale" in wikipedia, and then click on "english". Then also "Nebendiagonale" and other things get translated, like "antidiagonal, counter diagonal, secondary diagonal, trailing diagonal, minor diagonal" etc. – Dietrich Burde Mar 27 '18 at 12:40
  • Gerry says that the other Nebendiagonalen are called "broken diagonals", see this MSE-question, also found by google. – Dietrich Burde Mar 27 '18 at 12:44
  • This is just called the $(-k)$th diagonal in the Wolfram language documentation. http://reference.wolfram.com/language/ref/Diagonal.html – Travis Willse Mar 27 '18 at 13:31
  • @DietrichBurde I would expect "broken diagonal" to mean something like ${a_{i,j}:i-j\equiv k\pmod n}$, i.e., "diagonals" that, when reaching an edge of the matrix, continue from the opposite edge, resulting in a "break"in the picture. – Andreas Blass Mar 27 '18 at 14:49
  • @AndreasBlass You should address Gerry Myerson, not me. I agree with you. – Dietrich Burde Mar 27 '18 at 15:09

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