Linear Algebra

From David's Wiki
Jump to navigation Jump to search

Linear Algebra


Definiteness

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

Properties

  • 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

Examples of PSD matrices:

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