Notation for the Mixed Model This section introduces the mathematical notation used throughout this chapter to describe the mixed linear model. You should be familiar with basic matrix algebra (refer ...

The matrix Z can contain either continuous or dummy variables, just like X. The name mixed model comes from the fact that the model contains both fixed-effects parameters, , and random-effects ...

The R markdown document for this section is available here. Here we introduce the basics of matrix notation. Initially this may seem over-complicated, but once we discuss examples, you will appreciate ...

Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and ...

The impulse-momentum collision model of two vehicles-or any two bodies-is described in the literature, as a rule, in terms of planar mechanics. In the article a 3D generalization is presented in order ...

To solve this problem more efficiently, the WLS design of VFD FIR filters is formulated using matrix notation, and its optimality condition is established as a matrix equation. Then, a matrix ...

The final input line contains a expression in postfix notation. Each expression token is either a positive integer or one of the operators '+', '-' or '*'. Tokens are separated by a single space. In ...