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If T is a linear transformation of R^n, then the null space Null(T), also called the kernel Ker(T), is the set of all vectors X such that T(X)=0, i.e., Null(T)={X:T(X)=0}. ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

The odd divisor function sigma_k^((o))(n)=sum_(d|n; d odd)d^k (1) is the sum of kth powers of the odd divisors of a number n. It is the analog of the divisor function for odd ...

If a univariate real function f(x) has a single critical point and that point is a local maximum, then f(x) has its global maximum there (Wagon 1991, p. 87). The test breaks ...

Given a sample of n variates X_1, ..., X_N, reorder them so that Y_1<Y_2<...<Y_N. Then Y_i is called the ith order statistic (Hogg and Craig 1970, p. 146), sometimes also ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

A n×n matrix A is an orthogonal matrix if AA^(T)=I, (1) where A^(T) is the transpose of A and I is the identity matrix. In particular, an orthogonal matrix is always ...