Positive Definite Matrix
A Matrix 
is positive definite if
 | (1) |
. All Eigenvalues of a positive definite matrix arePositive (or, equivalently, the Determinants associated with all upper-leftSubmatrices are Positive).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) |
Symmetric Matrix | (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.
- Parallelogram
- Parallelogram Illusion
- Parallelogram Law
- Parallelohedron
- Parallelotope
- Parallel Postulate
- Parallel (Surface of Revolution)
- Paralogic Triangles
- Parameter
- Parameterization
- Parameter (Quadric)
- Parametric Latitude
- Parametric Test
- Pareto Distribution
- Parity
- Parity Constant
- Parking Constant
- Parodi's Theorem
- Parry Circle
- Parry Point
- Parseval's Integral
- Parseval's Relation
- Parseval's Theorem
- Partial Derivative
- Partial Differential Equation