##  [Macaulay Matrix](/macaulay-matrix) 

  ##  [Macaulay Matrix](https://algebra.quantumdictionary.io/macaulay-matrix-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A structured, often large, matrix whose rows are generated by multiplying input polynomials by monomials up to chosen degrees and whose columns are indexed by monomials; rank conditions and determinants/minors of this matrix encode solvability conditions, syzygies, and resultant information for polynomial systems.