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A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

For every infinite loop space machine E, there is a natural equivalence of spectra between EX and Segal's spectrum BX.

If two square n×n matrices A and B are simultaneously upper triangularizable by similarity transforms, then there is an ordering a_1, ..., a_n of the eigenvalues of A and ...

If a_1, a_2, a_3, ... is an artistic sequence, then 1/a_1, 1/a_2, 1/a_3, ... is a melodic sequence. The recurrence relation obeyed by melodic series is ...

A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

The series with sum sum_(n=0)^infty1/(F_(2^n))=1/2(7-sqrt(5)), where F_k is a Fibonacci number (Honsberger 1985).

A matrix with 0 determinant whose determinant becomes nonzero when any element on or below the diagonal is changed from 0 to 1. An example is M=[1 -1 0 0; 0 0 -1 0; 1 1 1 -1; ...

An image of an object obtained by reflecting it in a mirror so that the signs of one of its coordinates are reversed.

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least {1/3u(u-1)(u-2) for n=2u; 2/3u(u-1)(4u+1) for n=4u+1; ...