Chapter 18. Jacobians

  1. George A. F. Seber

Published Online: 8 JUN 2007

DOI: 10.1002/9780470226797.ch18

A Matrix Handbook for Statisticians

A Matrix Handbook for Statisticians

How to Cite

Seber, G. A. F. (2007) Jacobians, in A Matrix Handbook for Statisticians, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470226797.ch18

Author Information

  1. Department of Statistics University of Auckland, Auckland, New Zealand

Publication History

  1. Published Online: 8 JUN 2007
  2. Published Print: 7 NOV 2007

ISBN Information

Print ISBN: 9780471748694

Online ISBN: 9780470226797

SEARCH

Keywords:

  • jacobians;
  • statistical distribution theory;
  • differentiable functions;
  • differentials;
  • induced functional equations

Summary

This chapter contains sections titled:

  • Introduction

  • Method of Differentials

  • Further Techniques

  • Vector Transformations

  • Jacobians for Complex Vectors and Matrices

  • Matrices with Functionally Independent Elements

  • Symmetric and Hermitian Matrices

  • Skew-Symmetric and Skew-Hermitian Matrices

  • Triangular Matrices

  • Decompositions Involving Diagonal Matrices

  • Positive Definite Matrices

  • Caley Transformation

  • Diagonalizable Matrices

  • Pairs of Matrices