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The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

The conjugate gradient method is not suitable for nonsymmetric systems because the residual vectors cannot be made orthogonal with short recurrences, as proved in Voevodin ...

A bivector, also called a 2-vector, is an antisymmetric tensor of second rank (a.k.a. 2-form). For a bivector X^->, X^->=X_(ab)omega^a ^ omega^b, where ^ is the wedge product ...

A two-dimensional map which is conjugate to the Hénon map in its nondissipative limit. It is given by x^' = x+y^' (1) y^' = y+epsilony+kx(x-1)+muxy. (2)

Two complex numbers z=x+iy and z^'=x^'+iy^' are added together componentwise, z+z^'=(x+x^')+i(y+y^'). In component form, (x,y)+(x^',y^')=(x+x^',y+y^') (Krantz 1999, p. 1).

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

The contact angle between a sphere and a tangent plane is the angle alpha between the normal to the sphere at the point of tangency and the basal plane with respect to which ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...