Numerical Vectors

Abstract

This chapter is concerned with the linear algebra which is the mathematics which provides the foundation for understanding the machine learning algorithms. It is assumed that the input data is given as a numerical vector, in applying machine learning algorithms to real tasks. This chapter covers mainly the operations and the mathematical properties of the vector and the matrix, and the relation between them. We will mention the two schemes of reducing the dimension of the input vector: the singular value decomposition and the principal component analysis.

In Sect. 2.1, we introduce the numerical vectors by their concepts, and in Sect. 2.2, characterize the operations on them mathematically. In Sect. 2.3, we focus on the operations on matrices as the expansion from the vectors. In Sect. 2.4, we characterize the relation between vectors and matrices mathematically and in Sect. 2.5, we make the summarization on this chapter and the further discussions. This chapter is intended to characterize mathematically vectors and matrices as the foundation for understanding machine learning algorithms.