Definition of negative definite in English:

negative definite


  • 1(Of a function) having negative (formerly: negative or zero) values for all non-zero values of its argument.

  • 2(Of a square matrix) having all its eigenvalues negative.

  • 3(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 less than zero.


Mid 19th century; earliest use found in Proceedings of the Royal Society of London.