Sylvester's Criterion

Sylvester's Criterion is a mathematical test used to determine whether a symmetric matrix (like a grid of numbers) is positive definite. In simple terms, it helps check if certain related smaller matrices within the big matrix all have positive values when you calculate their determinants (a special number). If all these determinants are positive, then the entire matrix is positive definite. This concept is important in fields like optimization and statistics, where positive definiteness ensures, for example, that a function has a minimum point or a matrix modeling a system is stable.