linear algebra

Apples and oranges. Each element in a set is a pile containing some number of apples and some number of oranges.  Adding two piles means putting them together, resulting in a pile in the set. Multiplying a pile and a real number r means finding in the set a pile r times the amount.  We model each pile as a vector, and the set as a two-dimensional vector space over the field of real numbers.

Update on 9 April 2016.  At the bottom of this post, I attach a pdf file of my notes on scalar.

Notes on scalars now forms part of my notes on linear algebra.

Linear algebra is significant to many aspects of mechanics.  For some years I have been using the book by Shilov.  But this book may or may not be a good one to recommend to a student, depending on his or her prior experience.  On StackExchange Mathematics, there are several excellent threads discussing textbooks of linear algebra.  A particular recommendation was made for

Dear All,

How do find the inverse of the rectangular matrix.