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To truncate a real number is to discard its noninteger part. Truncation of a (positive) number x therefore corresponds to taking the floor function |_x_|. Truncation also ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

The Laplace-Carson transform F of a real-valued function f is an integral transform defined by the formula F(p)=pint_0^inftye^(-pt)f(t)dt. (1) In most cases, the function F ...

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

The absolute square of a complex number z, also known as the squared norm, is defined as |z|^2=zz^_, (1) where z^_ denotes the complex conjugate of z and |z| is the complex ...

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

The tetranacci numbers are a generalization of the Fibonacci numbers defined by T_0=0, T_1=1, T_2=1, T_3=2, and the recurrence relation T_n=T_(n-1)+T_(n-2)+T_(n-3)+T_(n-4) ...