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:

    In all cultures, the family imprints its members with selfhood. Human experience of identity has two elements; a sense of belonging and a sense of being separate. The laboratory in which these ingredients are mixed and dispensed is the family, the matrix of identity.
    Salvador Minuchin (20th century)

    Our role is to support anything positive in black life and destroy anything negative that touches it. You have no other reason for being. I don’t understand art for art’s sake. Art is the guts of the people.
    Elma Lewis (b. 1921)

    We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.
    Selma H. Fraiberg (20th century)

    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)