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Let P=p:q:r and U=u:v:w be distinct trilinear points, neither lying on a sideline of DeltaABC. Then the crossdifference of P and U is the point X defined by trilinears ...

Let A, B, and C be three polar vectors, and define V_(ijk) = |A_i B_i C_i; A_j B_j C_j; A_k B_k C_k| (1) = det[A B C], (2) where det is the determinant. The V_(ijk) is a ...

Given a differential p-form q in the exterior algebra ^ ^pV^*, its envelope is the smallest subspace W such that q is in the subspace ^ ^pW^* subset ^ ^pV^*. Alternatively, W ...

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

A binary Hamming code H_r of length n=2^r-1 (with r>=2) is a linear code with parity-check matrix H whose columns consist of all nonzero binary vectors of length r, each used ...

The Hilbert-Schmidt norm of a matrix A is a matrix norm defined by ||A||_(HS)=sqrt(sum_(i,j)a_(ij)^2).

The holomorphic tangent bundle to a complex manifold is given by its complexified tangent vectors which are of type (1,0). In a coordinate chart z=(z_1,...,z_n), the bundle ...

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...

Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...

A sum of the elements from some set with constant coefficients placed in front of each. For example, a linear combination of the vectors x, y, and z is given by ax+by+cz, ...