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König's line coloring theorem states that the edge chromatic number of any bipartite graph equals its maximum vertex degree. In other words, every bipartite graph is a class ...

The l^2-norm (also written "l^2-norm") |x| is a vector norm defined for a complex vector x=[x_1; x_2; |; x_n] (1) by |x|=sqrt(sum_(k=1)^n|x_k|^2), (2) where |x_k| on the ...

In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...

A Lehner continued fraction is a generalized continued fraction of the form b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...))) where (b_i,e_(i+1))=(1,1) or (2, -1) for x in [1,2) an ...

An ordering for the Cartesian product × of any two sets A and B with order relations <A and <B, respectively, such that if (a_1,b_1) and (a_2,b_2) both belong to A×B, then ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

A mathematical property P holds locally if P is true near every point. In many different areas of mathematics, this notion is very useful. For instance, the sphere, and more ...

A topology tau on a topological vector space X=(X,tau) (with X usually assumed to be T2) is said to be locally convex if tau admits a local base at 0 consisting of balanced, ...