plus a 13 left-parenthesis a 21 a 32 minus a 22 a 31 right-parenthesis period EndLayout"/>
Definition 2.13 (Positive definite matrix) A square
Example 2.8
Let
To show that
Therefore,
Definition 2.14 (Positive semidefinite matrix) A matrix
Definition 2.15 (Negative definite matrix) A square
Example 2.9
Let
To show that
Therefore,
Definition 2.16 (Negative semidefinite matrix) A matrix
We state the following theorem without proof.
Theorem 2.1
A 2 by 2 symmetric matrix
is:
1 positive definite if and only if and det
2 negative definite if and only if and det
3 indefinite if and only if det .
2.3 Random Variables and Distribution Functions
We begin this section with the definition of
Definition 2.17 (σ‐algebra) A
1 .
2 If then its complement .
3 If is a countable collection of sets in then their union .
Definition 2.18 (Measurable functions) A real‐valued function
