Linear Algebra Done Right Chapter 1

"Linear Algebra Done Right" is written by Professor Sheldon Alxer. I learned linear algebra when I was in engineering school, which more emphasizes the calculation side. Now I am relearning linear algebra in a different way from this book. 

What is vector space? 

Real number and Complex number. 

Definition of Complext number is an ordered pair (a, b) 

what does sqare root of -1 really mean? i * i = -1

use the ordered concept to describe the relationship between numbers. 

1.8 definition of list, length. 

in coding concept, set: no order; while list has order.