A Matrix
is positive definite if

(1) |

The Determinant of a positive definite matrix is Positive, but the converse is not necessarily true (i.e., a matrix with a Positive Determinant is not necessarily positive definite).

A Real Symmetric Matrix
is positive definite Iff there exists a Real nonsingular Matrix
such that

(2) |

(3) |

(4) |

A Hermitian Matrix is positive definite if

- 1. for all ,
- 2. for ,
- 3. The element of largest modulus must lie on the leading diagonal,
- 4. .

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1106, 1979.

© 1996-9

1999-05-26