Diagonally Dominant Matrix

Diagonally Dominant Matrix

In mathematics, a matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix A is diagonally dominant if

where aij denotes the entry in the ith row and jth column.

Note that this definition uses a weak inequality, and is therefore sometimes called weak diagonal dominance. If a strict inequality (>) is used, this is called strict diagonal dominance. The unqualified term diagonal dominance can mean both strict and weak diagonal dominance, depending on the context.

Read more about Diagonally Dominant Matrix:  Variations, Examples, Applications and Properties

Famous quotes containing the words dominant and/or matrix:

    What makes revolutionists is either self-pity, or indignation for the sake of others, or a sympathetic perception of the dominant undercurrent of progress in things. The nature before us is revolutionist from the direct sense of personal worth,... that pride of life, which to the Greek was a heavenly grace.
    Walter Pater (1839–1894)

    As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.
    Margaret Atwood (b. 1939)