Methods of Matrix Algebra

This book is designed to teach the thought and techniques of basic Matrix alge¬bra as a precise mathematical subject. Besides computational adeptness, there is an emphasis on uptake definitions and theorems, as well as reading, understand¬ing and creating proofs. A strictly logical organization, complete and exceed¬ingly detailed proofs of every theorem, suggestion on techniques for reading and handwriting proofs, and a variety of challenging theoretical exercises evidence slowly provide the novice with the tools and certainty to be able to study other mathematical topics in a rigorous fashion.In many respects this book is design for beginners. It combines an illustration hearted approach, well rounded explanations and wealth of practice opportuni¬ties. It makes a form friend for those students who are commencing a circuit in Matrix Algebra at school or for undergraduate series in Mathematics, Engineer¬ing or Physics.Applications of matrices are found in different scientific fields. In every field of physics, including classical mechanics, optics, electromagnetism and electrody¬namics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to manipulate 3D ideal and project them onto a 2-dimensional screen. Matrix calculus generalizes classical analyti¬cal notions such as derivatives and exponentials to higher dimensions. Matrices are used in economics to describe systems of economic relationships.Matrix calculations can be often performed with different techniques. Many problems can be solved by either direct algorithms or iterative approaches. For example, the eigenvectors of a square matrix can be obtained by discovery a sequence of vectors x_n converging to an eigenvector when n tends to infinity. Perhaps by providing a concise insight into where these concepts came from, how they were revealed, and how their uses in the past relate to how they are presently used and taught may offer students with the extra understanding they need to put these concepts to use, whether it be as measuring procedure, or as functions. With this better insight, one would be able to see the value in study¬ing trigonometry as an element of mathematics, instead of an isolated unit from the subject.This book aims to help the readers understand the wonderful world of Matrix Algebra, to enlighten them on how this subject having worth in real world problems.