Matrix Algebra

Matrices provide valuable tools for data representation, manipulation, and aid in pattern recognition. They are also used in data compression and neural networks. In order to fully appreciate their usefulness, we take a closer look at matrix algebra in this chapter. In the first part of the chapter, we review the basics of vector space algebra including algebraic bases and dimension. We discuss cosine similarity with an AI application to query matching, and take a look at determinants of square matrices. We then discuss special types of matrices and their factorizations, including the singular value decomposition and Cholesky factorization. We cover quaternions and rotation matrices, then convolutions of matrices with a view to their uses in AI.