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This post says

The main diagonal of a matrix consists of those elements that lie on the diagonal that runs from top left to bottom right.

Is it also clear when I rewrite that as

"The main diagonal of a matrix is the collection of entries that run from the top left to bottom right"?

Actually, the "collection of entries" is adapted from wikipedia

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  • That would be a matter of opinion. I personally find addition of redundant words makes things less clear. So, the original sentence is clearer. What are you adding by saying "collection of"? – urnonav Sep 25 '19 at 14:14
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Generally, sure. You can rewrite it as what you suggest.

Academically, no, you cannot interchange words in that way. As you get into a discipline, you have to use very controlled terminology. Synonyms for words may have a slightly nuanced and different meaning.

In math, a collection is a set of distinct objects. I have never seen elements of a matrix referred to as a collection, and I would you cannot call the elements in the main diagonal a collection. I have, however, seen a group of rows or columns referred to as a collection.

Entries can be used to describe a matrix's elements, but "elements" is more common.

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  • Right, but elements are not a collection of entries, right? In other words, elements or entries but not collection. The original does not say a set or collection. – Lambie Sep 25 '19 at 14:43
  • Actually, the "collection of entries" is adapted from wikipedia – user100097 Sep 26 '19 at 3:07

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