If A is positive definite, then
exists, and
is positive definite.

Name: If A is positive definite, then exists, and is positive definite.
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Question

If A is positive definite, then 
  exists, and 
  is positive definite.

Quizplus · Accepted Answer

Any positive definite matrix is invertible and its inverse is positive definite. Therefore, according to the given notation, 11edaba5_20b5_c4bf_a975_b1cd72c53c2a_TBMC1039_00 exists. Also, the Schur complement of a positive definite matrix is again positive definite, hence 11edaba5_20b5_c4c0_a975_01f3d73a570f_TBMC1039_00 is positive definite.

If a Is Positive Definite, Then