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If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

The Weyl tensor is the tensor C_(abcd) defined by R_(abcd)=C_(abcd)+2/(n-2)(g_(a[c)R_d]b-g_(b[c)R_(d]a)) -2/((n-1)(n-2))Rg_(a[c)g_(d]b), (1) where R_(abcd) is the Riemann ...

The Wolstenholme numbers are defined as the numerators of the generalized harmonic number H_(n,2) appearing in Wolstenholme's theorem. The first few are 1, 5, 49, 205, 5269, ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

About Eric Weisstein's World of Mathematics

Linear Algebra

The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

The Gegenbauer polynomials C_n^((lambda))(x) are solutions to the Gegenbauer differential equation for integer n. They are generalizations of the associated Legendre ...