1 is defined as A∈, if ≠ x∈, then AX > 0, then A is called a positive definite matrix and recorded as a ∈.

Remember ={A|≠ x∈, make AX > 0}.

Let definition 2 be A∈. If there is a positive diagonal matrix D= >0 for x ∈ and AX > 0, then A is called a generalized positive definite matrix, and it is denoted as a ∈. If D=

It has nothing to do with x, and it is recorded as A∈.

Remember the diagonal matrix d = {A∑|≠X] to make DAX >；; 0}.

Definition 3 let A∈, if =A, for ≠ x∈, there is ax >；; 0, then a is called a real symmetric positive definite matrix, and it is denoted as a ∈ s+.

Remember ={A∈|≠x, =A, make AX > 0}.

Let A∈ be defined in definition 4, if ≠X has S=∈ make DAX >；; 0, then a is called a generalized positive definite matrix, labeled as A∈, and if S= has nothing to do with x, labeled as a ∈.

Remember ={A∈|≠X, S=, makedax >; 0}.

Let A∈ be defined as 5, if all pairs of ≠ X∈ have S=. S+, so ax >；; 0, then a is called a generalized positive definite matrix, and denoted as A∈. If S= has nothing to do with x, it is recorded as a ∈.