Appendix A. Linear Algebra
Linear algebra is of primary importance in machine learning and it gives us an array of tools that are especially handy for the purpose of manipulating data and extracting patterns from it. Moreover, when data must be processed in batches as in much machine learning, great runtime efficiencies are gained from using the "vectorized" form as an alternative to traditional looping constructs when implementing software solutions in optimization or data pre-processing or any number of operations in analytics.
We will consider only the domain of real numbers in what follows. Thus, a vector 
represents an array of n real-valued numbers. A matrix 
is a two-dimensional array of m rows and n columns of real-valued numbers.
Some key concepts from the foundation of linear algebra are presented here.
Vector
The vector x (lowercase, bold, by convention; equivalently, 
) can be thought of as a point in n-dimensional space. Conventionally, we mean column-vector...
