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A square matrix A is a normal matrix if [A,A^(H)]=AA^(H)-A^(H)A=0, where [a,b] is the commutator and A^(H) denotes the conjugate transpose. For example, the matrix [i 0; 0 ...

The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...

Amazingly, the distribution of a sum of two normally distributed independent variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively is ...

Let A be a normed (Banach) algebra. An algebraic left A-module X is said to be a normed (Banach) left A-module if X is a normed (Banach) space and the outer multiplication is ...

In order to recover all Fourier components of a periodic waveform, it is necessary to use a sampling rate nu at least twice the highest waveform frequency. The Nyquist ...

An obelisk is a stone pillar erected as a monument that usually consists of a pyramid atop a tall square (or sometimes rectangular base). The elongated square pyramid can ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The operator norm of a linear operator T:V->W is the largest value by which T stretches an element of V, ||T||=sup_(||v||=1)||T(v)||. (1) It is necessary for V and W to be ...

The orthocentroidal circle of a triangle DeltaABC is a central circle having the segment joining the triangle centroid G and orthocenter H of DeltaABC as its diameter ...