n12 - Atsushi Inoue ECG 765: Mathematical Methods for...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Atsushi Inoue ECG 765: Mathematical Methods for Economics Fall 2009 Lecture Notes 12 Matrix Inverse, Matrix Rank and the Fundamental Theorem of Linear Algebra When we solve constraint optimization problems, one of the conditions, called constraint qualification, is often written in terms of rank. The inverse of a matrix is often used in graduate courses especially in econometrics. We will review these important concepts in matrix algebra. Outline A. Matrix Inverse B. Matrix Rank C. Fundamental Theorem of Linear Algebra A. Matrix Inverse Definition Let A be a square n n matrix. We shall say that A is invertible or non-singular if there exists an n n matrix B such that AB = BA = I n . This matrix B is called the inverse of A and is denoted by A- 1 . The matrix A- 1 is called A inverse. The inverse is unique if it exists. Example. A = " a b c d # . Theorem. (a) If A is invertible then so is A- 1 . The inverse of A- 1 is ( A- 1 )- 1 = A. 1 (b) If A and B are invertible then so is AB . The inverse of AB is ( AB )- 1 = B- 1 A- 1 . (c) If A is invertible, ( A- 1 ) > = ( A > )- 1 ....
View Full Document

Page1 / 5

n12 - Atsushi Inoue ECG 765: Mathematical Methods for...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online