Laplacian Matrix - As A Matrix Representation of The Negative Discrete Laplace Operator

As A Matrix Representation of The Negative Discrete Laplace Operator

The Laplacian matrix can be interpreted as a matrix representation of a particular case of the negative discrete Laplace operator. Such an interpretation allows one, e.g., to generalise the Laplacian matrix to the case of graphs with an infinite number of vertices and edges, leading to a Laplacian matrix of an infinite size.

Read more about this topic:  Laplacian Matrix

Famous quotes containing the words matrix, negative, discrete and/or laplace:

    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)

    The negative always wins at last, but I like it none the better for that.
    Mason Cooley (b. 1927)

    The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.
    W.V. Quine (b. 1908)

    Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.
    —Pierre Simon De Laplace (1749–1827)