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I have a non-square matrix $M$, that looks something like this:

$M=\left[ \begin{array} & a & b & c \\ d & e & f \\ g & h & i \\ j & k & l \\ \end{array}\right]$

I would like to refer the cells $M_{ij}$ where $i=j$, like $\{a,e,i\}$ in this case. If this was a square matrix, that would be the diagonal. Is that still the right word, or is there something more fitting that avoids confusion?

dimitriy
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    One can take a diagonal of the largest non-singular square submatrix to be the "main diagonal" – DVD May 13 '13 at 08:56

1 Answers1

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Yes, those entries: $m_{ij}$ in $M$, with $i = j$, constitute what can technically be called the "main diagonal" of the rectangular matrix, though the diagonal of such a matrix is not necessarily as "useful" as it is in a square matrix. See, e.g., the Main Diagonal entry in Wikipedia.

amWhy
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    Deserves a thumbs up! +1 – Amzoti May 13 '13 at 05:59
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    The Wikipedia page cites only Wolfram Alpha, which defines the "main diagonal" only for square matrices. I don't know how widely Wikipedia's definition is used. I recommend defining the term within any publication where you use this. – Josiah Yoder Jun 07 '21 at 18:51