Positive Semi-definite matrix

Definition:

A real symmetric m*m matrix K satisfying 


for all  (m-dimisionational vector a) is called a positive semi-definite matrix.


Theorems:

   (1) A real symmetric matrix is diagonalizable.

                                   Positive Semi-definite matrix_第1张图片

   (2) A real symmetric matrix is positive semi-definite if and only if all its eigenvalues are non-negative. 

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