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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 cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1,...,x_n} are the terms f_1 <= x_1<=g_1 (1) f_2(x_1) <= x_2<=g_2(x_1) (2) | ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. The ...

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 ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...

A generalization of the Bulirsch-Stoer algorithm for solving ordinary differential equations.

A second-order ordinary differential equation of the form