Introduction

A matrix is a rectangular array of numbers or expressions arranged in rows and columns and considered as a single entity. As we are considering a matrix as a single object, if we perform an operation on it, it will apply to each of the elements within it:

Figure 6.1: A simple m × n matrix with m rows and n columns

A simple linear single-dimension array rarely suffices for the physical world we live in, and almost all attributes related to space and time require more than one dimension. Compactness is one of the main reasons for the use of matrices. A matrix is compact when it is closed and bounded or simply has its points within a fixed distance of one another. Primarily for these two reasons, matrices find applications in practically every field, including fundamental mathematical concepts, ranging from graph theory, linear transformations, and probability theory, to different branches of physics, such as quantum mechanics and electromagnetism...