In mathematics, a moment matrix is a special symmetric square matrix whose rows and columns are indexed by monomials. 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 fitting, polynomial optimization (since positive semidefinite moment matrices correspond to polynomials which are sums of squares) and econometrics.

Application in regression

A multiple linear regression model can be written as

linear equations that can be expressed in matrix notation.

or

is the design matrix. Under the Gauss–Markov assumptions is the linear least squares defined as

and

is a square normal matrix.

See also

• Design matrix

• Gramian matrix

• Projection matrix

References

External links