Linear Algebra

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Linear Algebra


A square matrix is positive definite if for all vectors , .
If the inequality is weak () then the matrix is positive semi-definite.


  • If the determinant of every upper-left submatrix is positive then the matrix is positive-definite.
  • If is PSD then is PSD.
  • The sum of PSD matrices is PSD.


Examples of PSD matrices:

  • The identity matrix is PSD
  • is PSD for any vector