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enter image description here

Source: http://www.mathwords.com/a/area_convex_polygon.htm

What kind of determinant is that? Is there a standard convention to interpret determinants in that form?

Of course, looking at the expansion, one can guess that the same determinant could be written as a sum of $2\times2$ determinants but the I am concerned about the way it has been represented in the aforementioned website: whether it is a standard practice or not.

Yashas
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    This is not commonly used notation,. Most people would not call this operation "determinant", as it doesn't satisfy many of the desired properties determinants are expected to have. – vadim123 Apr 08 '17 at 15:03
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    What is that notation called? I was wondering if that website invented a new form of determinant or if such a representation already existed. – Yashas Apr 08 '17 at 15:04
  • I, personally, have never seen this operation, with any notation. – vadim123 Apr 08 '17 at 15:05

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This is known as the shoelace formula.

Alain
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