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Let R(x) be the revenue for a production x, C(x) the cost, and P(x) the profit. Then P(x)=R(x)-C(x), and the marginal profit for the x_0th unit is defined by ...

The Diophantine equation x^2+y^2+z^2=3xyz. The Markov numbers m are the union of the solutions (x,y,z) to this equation and are related to Lagrange numbers.

A type I move (conjugation) takes AB->BA for A, B in B_n where B_n is a braid group. A type II move (stabilization) takes A->Ab_n or A->Ab_n^(-1) for A in B_n, and b_n, Ab_n, ...

A spectrum containing the real numbers larger than Freiman's constant.

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...

The term "math" is the usual term for "mathematics" used in the United States. In contrast, the term "maths" is used in the United Kingdom.

The term "maths" is the usual term for "mathematics" used in the United Kingdom. In contrast, the term "math" is used in the United States.

Denote the sum of two matrices A and B (of the same dimensions) by C=A+B. The sum is defined by adding entries with the same indices c_(ij)=a_(ij)+b_(ij) over all i and j. ...

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.

The matrix direct sum of n matrices constructs a block diagonal matrix from a set of square matrices, i.e., direct sum _(i=1)^nA_i = diag(A_1,A_2,...,A_n) (1) = [A_1 ; A_2 ; ...