Positive definite
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
A symmetric matrix all of whose eigenvalues are strictly positive, equivalently one whose associated quadratic form is always strictly positive; the required property of a covariance matrix for strict optimization.
Positive definite in plain English
'Positive definite' is a stamp of approval on a certain kind of square grid of numbers (a matrix), and for finance it usually describes a covariance matrix, which records how a bunch of investments move together. Being positive definite means the matrix is well-behaved: every possible mix of those investments has a genuinely positive amount of risk, never zero and never a nonsensical 'negative risk.' Think of it as the guarantee that no matter how you blend your ingredients, the recipe still makes sense. Optimizers that build 'best' portfolios need this property, because without it the math can spit out impossible or unstable answers.
Learn these first
Related Quantitative Finance terms
Quantitative Finance practice questions · Quantitative Finance flashcards · Quantitative Finance study guide