A symmetric matrix
is positive definite if and only if
is negative definite.

Question

A symmetric matrix 
  is positive definite if and only if 
  is negative definite.

Quizplus · Accepted Answer

This is a property of symmetric matrices: if a matrix A is positive definite, then its negative -A is negative definite. Similarly, if A is negative definite, then -A is positive definite. This is because the eigenvalues of A and -A are opposite in sign. Therefore, if 11edaba5_20b5_c4c2_a975_412b8aa16d43_TBMC1039_00 is positive definite, then -11edaba5_20b5_c4c3_a975_4d8b1a7e0bf4_TBMC1039_00 is negative definite.

A Symmetric Matrix