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An operation that takes two vector bundles over a fixed space and produces a new vector bundle over the same space. If E_1 and E_2 are vector bundles over B, then the Whitney ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...

A vector sum is the result of adding two or more vectors together via vector addition. It is denoted using the normal plus sign, i.e., the vector sum of vectors A, B, and C ...

S_n=sum_(i)eta_imu(E_i), where mu(E_i) is the measure of the set E_i of points on the x-axis for which f(x) approx eta_i.

A cumulative sum is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence {a,b,c,...}, are a, a+b, a+b+c, .... Cumulative sums are ...

There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

The sum rule for differentiation states d/(dx)[f(x)+g(x)]=f^'(x)+g^'(x), (1) where d/dx denotes a derivative and f^'(x) and g^'(x) are the derivatives of f(x) and g(x), ...

The connected sum M_1#M_2 of n-manifolds M_1 and M_2 is formed by deleting the interiors of n-balls B_i^n in M_i^n and attaching the resulting punctured manifolds M_i-B^._i ...