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The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

The cototient of a positive number n is defined as n-phi(n), where n is the totient function. It is therefore the number of positive integers <=n that have at least one prime ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

The elliptic hyperboloid is the generalization of the hyperboloid to three distinct semimajor axes. The elliptic hyperboloid of one sheet is a ruled surface and has Cartesian ...

Elliptic rational functions R_n(xi,x) are a special class of rational functions that have nice properties for approximating other functions over the interval x in [-1,1]. In ...

A problem listed in a fall issue of Gazeta Matematică in the mid-1970s posed the question if x_1>0 and x_(n+1)=(1+1/(x_n))^n (1) for n=1, 2, ..., then are there any values ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...