For several topics in this book, we used principles, concepts, and results from the field of matrix algebra. In this appendix, we provide a review of matrix algebra.

Consider a data series *x* = {*x*_{1}, *x*_{2}, ..., *x*_{n}} of size *n*. Instead of the complicated notation using commas between the individual observations, we could write the *n* observations in terms of vector notation as follows

**Equation B.1. **

where the left side in equation (B.1) denotes *x* as a *column vector* while the right side denotes it as a *row vector*. Both vectors are of length *n* (coordinates) since all observations have to be accounted for. Note that the right (row) vector is the *transpose* of the left (column) vector and vice versa. The transpose is obtained by simply turning the vector by 90 degrees, which is indicated by the upper index *T*. We could have defined *x* as a row vector instead and the transpose would then be the column vector. By doing so, we shift the *dimensionality* of the vectors. The column vector is often indicated by the size *n* × 1 meaning *n* rows and 1 column. A row vector is indicated by size 1 × *n* meaning just one row and *n* columns.

Suppose there is a second series of observations of the same length *n* as *x*, say *y* = (*y*_{1}, *y*_{2}, ..., *y*_{n}). This second series of observation could be written as a vector. However, *x* and *y* could both ...

Start Free Trial

No credit card required