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

  • Thread starter Thread starter colstat
  • Start date Start date
  • Tags Tags
    Matrix Positive
colstat
Messages
56
Reaction score
0
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?
 
Physics news on Phys.org
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?
 
HallsofIvy said:
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?

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.
 
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.
 
The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...
Back
Top