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A four-vector a_mu is said to be lightlike if its four-vector norm satisfies a_mua^mu=0. One should note that the four-vector norm is nothing more than a special case of the ...

A linear system of equations is a set of n linear equations in k variables (sometimes called "unknowns"). Linear systems can be represented in matrix form as the matrix ...

The vector space generated by the rows of a matrix viewed as vectors. The row space of a n×m matrix A with real entries is a subspace generated by n elements of R^m, hence ...

A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

The characteristic function f(n)={1 n is prime; 0 n otherwise (1) of primes has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051) for n=1, 2, ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. B. Haible and T. Papanikolaou computed zeta(3) to 1000000 ...

A number n is k-multiperfect (also called a k-multiply perfect number or k-pluperfect number) if sigma(n)=kn for some integer k>2, where sigma(n) is the divisor function. The ...

A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...