Talk:Diagonally dominant matrix

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ith

Putting a space between "i" and "th" may improve readability in many browsers, but it isn't correct; "i" and "th" aren't separate words. You might put a hyphen, but I don't think that's terribly common. As an example, Strang's "Linear Algebra" uses "ith" and not "i-th".

As an alternative for readability in browsers, the sentence could be reworded to use the phrase "row i and column j" instead. Lunch 21:14, 23 August 2006 (UTC)

Another alternative that might not be terribly in common (I don't know) would be to put the th as a superscript as in ith ArkianNWM (talk) 05:50, 26 April 2009 (UTC)

Variations

In case the term "strictly diagonally dominant" is used, then the matrices for which the conditions is satisfied for are usually called simply "diagonally dominant", and not "weakly diagonally dominant". It might be useful to include this in the article, since it can easily cause misinterpretations. Lp82 (talk) 08:17, 15 October 2008 (UTC)

Correct. I added a sentence to the article, but please feel free to improve on it. -- Jitse Niesen (talk) 12:24, 15 October 2008 (UTC)

Examples

Although this concept is not complex, a lack of examples makes it more difficult to initially understand. Since there are no examples of diagonally dominant matrices on the page, I propose adding a section with at least one example. Most likely more than one example would be necessary, one for a strictly diagonally dominant matrix and one for a diagonally dominant matrix that is not strictly diagonally dominant. —Preceding unsigned comment added by Neoleex (talkcontribs) 23:49, 27 April 2009 (UTC)

Properties

I would like to see a reference to a proof for this:

A Hermitian diagonally dominant matrix with real non-negative diagonal entries is positive semi-definite. If the symmetry requirement is eliminated, such a matrix is not necessarily positive semi-definite; however, the real parts of its eigenvalues are non-negative. — Preceding unsigned comment added by 193.71.203.67 (talk) 08:25, 20 February 2012 (UTC)

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