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 |