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Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

The Hermite polynomials H_n(x) are set of orthogonal polynomials over the domain (-infty,infty) with weighting function e^(-x^2), illustrated above for n=1, 2, 3, and 4. ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

The parameter r in the exponential equation of population growth N(t)=N_0e^(rt), where N_0 is the initial population size (at t=0) and t is the elapsed time.

A polynomial equation whose roots all have negative real parts. For a real quadratic equation z^2+Bz+C=0, the stability conditions are B,C>0. For a real cubic equation ...

A polynomial discriminant is the product of the squares of the differences of the polynomial roots r_i. The discriminant of a polynomial is defined only up to constant ...

Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...