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A square matrix with constant skew diagonals. In other words, a Hankel matrix is a matrix in which the (i,j)th entry depends only on the sum i+j. Such matrices are sometimes ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

A technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Cayley (1845) originally coined the term, but subsequently used it to refer ...

An identity is a mathematical relationship equating one quantity to another (which may initially appear to be different).

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

The n functions f_1(x), f_2(x), ..., f_n(x) are linearly dependent if, for some c_1, c_2, ..., c_n in R not all zero, sum_(i=1)^nc_if_i(x)=0 (1) for all x in some interval I. ...

A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

The (signed) area of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) is A=1/2(|x_1 x_2; y_1 y_2|+|x_2 x_3; y_2 y_3|+...+|x_n x_1; y_n y_1|), ...