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A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements. The number of zeros a matrix needs ...

A square matrix A is a special orthogonal matrix if AA^(T)=I, (1) where I is the identity matrix, and the determinant satisfies detA=1. (2) The first condition means that A ...

A square matrix U is a special unitary matrix if UU^*=I, (1) where I is the identity matrix and U^* is the conjugate transpose matrix, and the determinant is detU=1. (2) The ...

A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

The Laplacian spectral ratio R_L(G) of a connected graph G is defined as the ratio of its Laplacian spectral radius to its algebraic connectivity. If a connected graph of ...

In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

Let k be a field of finite characteristic p. Then a polynomial P(x) in k[x] is said to be additive iff P(a)+P(b)=P(a+b) for {a,b,a+b} subset k. For example, P(x)=x^2+x+4 is ...

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...