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Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...

A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal (i.e., along the subdiagonal and superdiagonal), [a_(11) ...

Delta(x_1,...,x_n) = |1 x_1 x_1^2 ... x_1^(n-1); 1 x_2 x_2^2 ... x_2^(n-1); | | | ... |; 1 x_n x_n^2 ... x_n^(n-1)| (1) = product_(i,j; i>j)(x_i-x_j) (2) (Sharpe 1987). For ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

There are at least two distinct notions known as the Whitehead group. Given an associative ring A with unit, the Whitehead group associated to A is the commutative quotient ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...