Summary

In this chapter, we introduced the basics of linear algebra, including working with vectors and matrices and performing matrix-vector multiplication. We highlighted a few special matrices, such as the identity matrix, and common operations, such as transposing and inverting a matrix.

Next, we used matrix-vector multiplication to solve a system of linear equations under different settings. We introduced the geometric interpretation that corresponds to the system of linear equations, along with how to obtain the solution using matrix inverse and multiplication operations.

Lastly, we touched upon common settings of the input matrix in the machine learning context, covering both underdetermined and overdetermined systems. Developing such an understanding will be crucial when we delve into statistical modeling and machine learning in the third part of this book.

In the next chapter, we will discuss slightly more advanced concepts in matrix algebra and implementations in...