Kronecker Products and Matrix Calculus with Applications — A. Graham

This little book is quite dense and wastes no time on wordiness. Its compact nature packs a lot of useful matrix calculus into just over 100 pages with no frills, yet still manages to give a decent number of examples to illustrate concepts, including applications (most in the multivariate statistics realm). For engineers especially who need to learn how to do some matrix calculus, this is a good resource. Mathematicians interested in proofs and deeper notions may find it a bit lacking in the regard and should probably supplement with another text to pursue this subject more deeply. Overall, I found it definitely worth the read, and now have a great little resource for those times when I need to recall some tricks. Solutions to problems are given in the text, and the bibliography is short but good. 

Review

Prerequisites

calculus, matrix algebra, some linear algebra is helpful

Topics Covered

  • matrix decomposition
  • vec operator
  • Kronecker product and Kronecker sum (properties, rules, etc)
  • applications of the Kronecker product in solving linear systems and differential equations
  • derivatives of vectors
  • derivative of scalar functions with respect to a matrix
  • derivative of matrix with respect to one of its elements and conversely
  • derivatives of matrix powers
  • matrix differential
  • derivative of a matrix with respect to a matrix
  • applications
    • least squares
    • constrained optimization
    • maximum likelihood estimation of multivariate normal distribution
    • Jacobians of transformations

Attributes

Difficulty 2
Good for teaching? 4
Proof Quality 2
Quality of Exercises 4
Self-Study 3
Readability 4