Search Results for ""

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

The notion of a Hilbert C^*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by Kaplansky (1953). The research on Hilbert ...

The Mordell conjecture states that Diophantine equations that give rise to surfaces with two or more holes have only finite many solutions in Gaussian integers with no common ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

The constant s_0 in Schnirelmann's theorem such that every integer >1 is a sum of at most s_0 primes. Of course, by Vinogradov's theorem, it is known that 4 primes suffice ...

Analysis

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...