Definition of positive definite in US English:

positive definite


  • (Of a function) having positive (formerly, positive or zero) values for all non-zero values of its argument; (of a square matrix) having all its eigenvalues positive; (more widely, of an operator on a Hilbert space) such that the inner product of any element of the space with its image under the operator is greater than zero.


Early 20th century; earliest use found in Transactions of the American Mathematical Society.