Moment matrix
Encyclopedia
In mathematics
, a moment matrix is a special symmetric square matrix
whose rows and columns are indexed by monomial
s. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.)
Moment matrices play an important role in polynomial optimization, since positive semidefinite moment matrices correspond to polynomials which are sums of squares.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a moment matrix is a special symmetric square matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
whose rows and columns are indexed by monomial
Monomial
In mathematics, in the context of polynomials, the word monomial can have one of two different meanings:*The first is a product of powers of variables, or formally any value obtained by finitely many multiplications of a variable. If only a single variable x is considered, this means that any...
s. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.)
Moment matrices play an important role in polynomial optimization, since positive semidefinite moment matrices correspond to polynomials which are sums of squares.