Positive Definite Matrix

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 matrixwith 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.

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