How do I

**determine if a matrix is positive definite**using**MATLAB**? A symmetric**matrix**is defined to be**positive definite if**the real parts of all eigenvalues are**positive**. A non-symmetric**matrix**(B) is**positive definite if**all eigenvalues of (B+B')/2 are**positive**.Similarly one may ask, can a singular matrix be positive definite?

Singularity

**positive semidefinite**. The determinant of a**matrix**equals the product of its eigenvalues. A**positive semidefinite matrix**is a symmetric**matrix**with only nonnegative eigenvalues. A**positive definite matrix**is a symmetric**matrix**with only**positive**eigenvalues.Secondly, what is a non positive definite matrix?

3. 31. The covariance

**matrix**is**not positive definite**because it is singular. That means that at least one of your variables can be expressed as a linear combination of the others. You do**not**need all the variables as the value of at least one can be determined from a subset of the others.Is a transpose a positive definite?

Now AT is the

**transpose**of A. This means the columns of AT are formed with the corresponding rows of A.**Positive definite**means that xTAx >0 for allx≠0. Also with square symmetric matrices, the quadratic form xTAx is**positive definite**if and only if the eigenvalues of A are all**positive**.What is meant by singular matrix?

**Singular Matrix**. A square

**matrix**that does not have a

**matrix**inverse. A

**matrix**is

**singular**iff its determinant is 0.