Talk:Diagonally dominant matrix

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)[reply]

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

Variations

In case the term "strictly diagonally dominant" is used, then the matrices for which the conditions is satisfied for $\geq$ 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)[reply]

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)[reply]

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 (talk • contribs) 23:49, 27 April 2009 (UTC)[reply]

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)[reply]