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Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...

A number of attractive 60-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

Arrange copies of the n digits 1, ..., n such that there is one digit between the 1s, two digits between the 2s, etc. For example, the unique (modulo reversal) n=3 solution ...

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 ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...

Given a factor a of a number n=ab, the cofactor of a is b=n/a. A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor M_(ij) defined ...

Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...

Given a formula y=f(x) with an absolute error in x of dx, the absolute error is dy. The relative error is dy/y. If x=f(u,v,...), then ...