# n8 - Atsushi Inoue ECG 765 Mathematical Methods for...

This preview shows pages 1–3. Sign up to view the full content.

Atsushi Inoue ECG 765: Mathematical Methods for Economics Fall 2009 Lecture Notes 8 Determinantal Tests of Definiteness To test the second-order sufficient condition we need to find out the definite- ness of the Hessian matrix of an objective function. There are two commonly used methods to test definiteness of a matrix. One is based on determinants and another is on eigenvalues. Outline A. Determinants B. Principal Minors and Definiteness A. Determinants Definition. Let A = " a b c d # be a 2 × 2 matrix. We define its determinant to be ad - bc . The determinant of A is written in two ways, det A and | A | . Definition. Let A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 be a 3 × 3 matrix. We define its determinant according to the formula as the expansion by a row, say the first row. That is, we define det A = a 11 a 22 a 23 a 32 a 33 - a 12 a 21 a 23 a 31 a 33 + a 13 a 21 a 22 a 31 a 32 = a 11 | A 11 | - a 12 | A 12 | + a 13 | A 13 | . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
where A ij is the matrix obtained from A by deleting the i -th row and the j -th column.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern