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The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

The successive overrelaxation method (SOR) is a method of solving a linear system of equations Ax=b derived by extrapolating the Gauss-Seidel method. This extrapolation takes ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

Given a polynomial p(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 (1) of degree n with roots alpha_i, i=1, ..., n and a polynomial q(x)=b_mx^m+b_(m-1)x^(m-1)+...+b_1x+b_0 (2) of ...