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Given a quadratic form Q(x,y)=x^2+y^2, (1) then Q(x,y)Q(x^',y^')=Q(xx^'-yy^',x^'y+xy^'), (2) since (x^2+y^2)(x^('2)+y^('2)) = (xx^'-yy^')^2+(xy^'+x^'y)^2 (3) = ...

Conditional logit regression assumes a model of the form p_j=(e^(beta^'x_j))/(sum_(j)e^(beta^'x_j)) for j=1, ..., k+1. In this model, a subject is presented with choice ...

K=-e^2, where e is the eccentricity of a conic section.

The number of elements of a group in a given conjugacy class.

A type I Markov move.

A topological space.

An immediate consequence of a result already proved. Corollaries usually state more complicated theorems in a language simpler to use and apply.

x^(2n)+1=[x^2-2xcos(pi/(2n))+1] ×[x^2-2xcos((3pi)/(2n))+1]×...× ×[x^2-2xcos(((2n-1)pi)/(2n))+1].

If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

Exchanges branches of the hyperbola x^'y^'=xy. x^' = mu^(-1)x (1) y^' = -muy. (2)