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Let X be a normed space and X^(**)=(X^*)^* denote the second dual vector space of X. The canonical map x|->x^^ defined by x^^(f)=f(x),f in X^* gives an isometric linear ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

An SIR model is an epidemiological model that computes the theoretical number of people infected with a contagious illness in a closed population over time. The name of this ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

The Lie derivative of a spinor psi is defined by L_Xpsi(x)=lim_(t->0)(psi^~_t(x)-psi(x))/t, where psi^~_t is the image of psi by a one-parameter group of isometries with X ...

The square root method is an algorithm which solves the matrix equation Au=g (1) for u, with A a p×p symmetric matrix and g a given vector. Convert A to a triangular matrix ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...