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A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

Sequences x_n^((1)), x_n^((2)), ..., x_n^((k)) are linearly dependent if constants c_1, c_2, ..., c_k (not all zero) exist such that sum_(i=1)^kc_ix_n^((i))=0 for n=0, 1, ....

For a given function f(x) over a partition of a given interval, the lower sum is the sum of box areas m^*Deltax_k using the infimum m of the function f(x) in each subinterval ...

Denote the sum of two matrices A and B (of the same dimensions) by C=A+B. The sum is defined by adding entries with the same indices c_(ij)=a_(ij)+b_(ij) over all i and j. ...

The mean tetrahedron volume V^_ is the average volume of a tetrahedron in tetrahedron picking within some given shape. As summarized in the following table, it is possible to ...

The minimal residue of a (mod m) is the value b or b-m, whichever is smaller in absolute value, where a=b (mod m). If m=2b (so that b=|b-m|), then the minimal residue is ...

The upside-down capital delta symbol del , also called "del," used to denote the gradient and other vector derivatives. The following table summarizes the names and notations ...

If A=>!B and B=>!A (i.e., (A=>!B) ^ (B=>!A), where !A denotes NOT, => denotes implies, and ^ denotes AND), then A and B are said to be inequivalent, a relationship which is ...

There are a number of attractive polyhedron compounds consisting of nine octahedra. The compound illustrated above can be constructed as the dual of cube 9-compound. The ...

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.