December 2019
Intermediate to advanced
960 pages
25h 46m
English
Content preview from Essentials of Mathematical Methods in Science and Engineering, 2nd Edition
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
CHAPTER 5LINEAR ALGEBRA
Vectors are usually introduced with their geometric definition as directed line segments. Introduction of a coordinate system allows the concept of vector to be extended to a much broader class of objects called tensors, which are defined in terms of their transformation properties. As a tensor, vectors are now classified as first‐rank tensors. In 
dimensions, a given vector can be written as the linear combination of 
linearly independent basis vectors. Linear algebra is essentially the branch of mathematics that uses the concept of linear combination to extend the vector concept to a much broader class of objects. In this chapter, we discuss abstract vector spaces, which paves the way to many scientific and engineering applications of linear algebra.
5.1 FIELDS AND VECTOR SPACES
We start with the basic definitions used throughout this chapter [1–3]. As usual, a collection of objects is called a set. The set of all real numbers is denoted by 
and the set of all complex numbers by 
. The set of all ‐tuples of real numbers,
(5.1)
is shown by . Similarly, the ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.