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If a matrix A has a matrix of eigenvectors P that is not invertible (for example, the matrix [1 1; 0 1] has the noninvertible system of eigenvectors [1 0; 0 0]), then A does ...

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

The Fano plane is the configuration consisting of the two-dimensional finite projective plane over GF(2) ("of order two"), illustrated above. It is a block design with nu=7, ...

In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row ...

Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

An inequality which implies the correctness of the Robertson conjecture (Milin 1964). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach ...

A coordinate system (mu,nu,psi) defined by the coordinate transformation x = (munu)/((mu^2+nu^2)^2)cospsi (1) y = (munu)/((mu^2+nu^2)^2)sinpsi (2) z = ...

A coordinate system (mu,nu,psi) given by the coordinate transformation x = (mucospsi)/(mu^2+nu^2) (1) y = (musinpsi)/(mu^2+nu^2) (2) z = nu/(mu^2+nu^2) (3) and defined for ...

A logical system which possesses an explicitly stated set of axioms from which theorems can be derived.

The system of partial differential equations u_t+u_x = v^2-u^2 (1) v_t-v_x = u^2-v^2. (2)