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A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...

An invertible linear transformation T:V->W is a map between vector spaces V and W with an inverse map which is also a linear transformation. When T is given by matrix ...

The term used in physics and engineering for a harmonic function. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...