A Welcome from David
Hello everybody! I am very happy that you chose to go through my note.
Linear algebra is a fantastic branch of math and no need to say, most of the students don’t understand what is going on even after the final exam of freshman yea’s linear algebra.
I want this note to be useful to you if you are a grade 12 student, and you are willing to challenge yourself. Or you could be a first-year university student struggling in this course and you want to pass the course.
Or you could be a second or third-year STEM student and already learned all the concepts but willing to get a better understanding of how linear algebra applies in your field.
Finally, I also want this note to be useful even if you are a TA or a high school teacher who teaches relevant concepts. so you might find some new perspectives or interesting examples that you can apply in your own teaching.
What can you get from this note
First of all, Linear algebra meant to be a university-level course, so you should understand is that the course itself is not easy. Also, since Linear algebra has impacts on so many fields such as statistics, economy, physics, computer science, this note will touch many different concepts/examples from other fields.
Nevertheless, this is a “note” of linear algebra, one should not expect to only use this as the reference. However, this note can give you an easier, more practical approach to linear algebra.
Instead of introducing all the different concepts from nothing and forcing students to memorize the detail, we are trying something different here.
Every chapter will begin with motivation and each concept will be explained not by proof. To see the proof, you can go through the textbook or search online. Here, we only focus on the true purpose of introducing the new idea and how is this new idea helps us in different ways.
Of course, practice makes perfect, so each chapter will be followed by a relatively big problem set. Each of the questions in the problem set will have a simple explanation.
Hopefully, everyone can get a much better understanding after reading the note and be able to perform some useful calculations. In the end, I would like to quote what Dieudonné said in his “Foundations of Modern Analysis, Vol. 1”:
There is hardly any theory which is more elementary (than linear algebra), in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices.