Appendix A

Theoretical foundations

A.1 Matrix Algebra

Basic Manipulations and Properties

A column vector x with d dimensions can be written



where the transpose operator, superscript T, allows it be written as a transposed row vector—which is useful when defining vectors in running text. In this book, vectors are assumed to be row vectors.

The transpose AT of a matrix A involves copying all the rows of the original matrix A into the columns of AT. Thus a matrix with m rows and n columns becomes a matrix with n rows and m columns:


The dot product

Get Data Mining, 4th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.