# How to make matrix positive definite (when it is not)?

1. Apr 23, 2012

### colstat

Suppose I have a matrix that looks like this
[,1] [,2]
[1,] 2.415212e-09 9.748863e-10
[2,] -2.415212e-09 5.029136e-10

How do I make it positive definite? I am not looking for specific numerical value answer, but a general approach to this problem.

I have heard singular value decomposition, or getting some eigenvalue? Is that correct?

2. Apr 24, 2012

### HallsofIvy

Staff Emeritus
What do you mean by "make" a matrix positive definite? Since this matrix is NOT positive definite you must mean to change it into one that is. What is the relationship of this new matrix to the original supposed to be?

3. Apr 24, 2012

### colstat

I was hoping to "make" it positive using some trick, but after looking around again I am wrong. Like you said, if it's NOT positive definite, then it's not.

I also realized there's an error when putting together the matrix. So, problem solved I guess.

4. Apr 25, 2012

### FoldHellmuth

From an engineer point of view what I would do if I had a non-positive definite matrix is:
1. Obtain its eigen decomposition.
2. Changes the negative eigenvalues for zeroes.