December 2019
Intermediate to advanced
960 pages
25h 46m
English
Content preview from Essentials of Mathematical Methods in Science and Engineering, 2nd Edition
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CHAPTER 4DETERMINANTS AND MATRICES
In many areas of mathematical analysis, we encounter systems of ordered sets of elements, which could be sets of numbers, functions, or even equations. Determinants and matrices provide an elegant and an efficient computational tool for handling such systems. We already used some of the basic properties of matrices and determinants when we discussed coordinate systems and tensors. In this chapter, we give a formal treatment of matrices and determinants and their applications to systems of linear equations.
4.1 BASIC DEFINITIONS
We define a rectangular matrix of dimension 
as an array [1]
(4.1)
where the elements of 
could be numbers, functions, or even other matrices. An alternate way to write a matrix is
(4.2)
where 
is called the 
th element or the component of . The first subscript denotes the row number, and the second subscript denotes the ...
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