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An n×n square matrix M with M_(ii) = 1 (1) M_(ij) = M_(ji)>1 (2) for all i,j=1, ..., n.

The radial curve of the cycloid with parametric equations x = a(t-sint) (1) y = a(1-cost) (2) is the circle x_r = x_0+2asint (3) y_r = -2a+y_0+2acost. (4)

The cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1,...,x_n} are the terms f_1 <= x_1<=g_1 (1) f_2(x_1) <= x_2<=g_2(x_1) (2) | ...

A polyhedral graph having 10 vertices. There are 32300 nonisomorphic nonahedral graphs, as first enumerated by Duijvestijn and Federico (1981).

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

Given a square matrix M, the following are equivalent: 1. |M|!=0. 2. The columns of M are linearly independent. 3. The rows of M are linearly independent. 4. Range(M) = R^n. ...

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

Two quantities are said to be different (or "unequal") if they are not equal. The term "different" also has a technical usage related to modules. Let a module M in an ...

A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.