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In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. [1]
With some standard function when there is little chance of ambiguity, it is common to omit the parentheses around the argument altogether (e.g., ). Note that this is never done with a general function f {\displaystyle f} , in which case the parenthesis are always included
is the unit circle in P 2 = is the unit hyperbola in P 2. + + + = gives the Fermat cubic surface in P 3 with 27 lines. The 27 lines in this example are easy to describe explicitly: they are the 9 lines of the form (x : ax : y : by) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
The definition in the first paragraph sums entries across each row. It is therefore sometimes called row diagonal dominance. If one changes the definition to sum down each column, this is called column diagonal dominance. Any strictly diagonally dominant matrix is trivially a weakly chained diagonally dominant matrix.
The formula developed by Aumann and Shapley to construct a Shapley value for non atomic games with a continuum of players Topics referred to by the same term This disambiguation page lists articles associated with the title Diagonal formula .
= and the power of a diagonal matrix can be calculated by taking the corresponding powers of the diagonal entries, which is much easier than doing the exponentiation for A instead. This can be used to compute the matrix exponential e A , a need frequently arising in solving linear differential equations , matrix logarithms and square roots of ...
Matrix diagonalization, a construction of a diagonal matrix (with nonzero entries only on the main diagonal) that is similar to a given matrix; Diagonal argument (disambiguation), various closely related proof techniques, including: Cantor's diagonal argument, used to prove that the set of real numbers is not countable
A band matrix with k 1 = k 2 = 0 is a diagonal matrix, with bandwidth 0. A band matrix with k 1 = k 2 = 1 is a tridiagonal matrix, with bandwidth 1. For k 1 = k 2 = 2 one has a pentadiagonal matrix and so on. Triangular matrices. For k 1 = 0, k 2 = n−1, one obtains the definition of an upper triangular matrix