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A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

An integer N which is a product of distinct primes and which satisfies 1/N+sum_(p|N)1/p=1 (Butske et al. 1999). The first few are 2, 6, 42, 1806, 47058, ... (OEIS A054377). ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...

A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...

The vector space generated by the rows of a matrix viewed as vectors. The row space of a n×m matrix A with real entries is a subspace generated by n elements of R^m, hence ...

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification ...

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 ...