Application of linear algebra Pdf

This eBook provides an overview of linear algebra, including a discussion on the role of linear algebra in mathematics and its applications. After a general introduction to linear algebra, the book gives a historical background from the 18th-century French mathematician G.B. Jerrard and his contribution to the development of linear algebra. Then the notion of vector spaces is discussed in detail, covering topics such as subspaces, bases and dimension. The module continues with the notions of inner products and norms of vectors, followed by Gram-Schmidt orthogonalization and Hilbert spaces. The text also explains concepts such as norms and quadratic forms. Additional topics covered include change of basis, similarity spaces, eigenvalues and eigenvectors, diagonalization of matrices, LU-decomposition, computation geometry and projections onto convex sets or onto an affine subspace. The module concludes with a section concerning the main applications of linear algebra in other disciplines such as science, engineering and finance

Linear algebra is a fundamental branch of mathematics for applied mathematics and science. Linear algebra is also used in many famous problems in theoretical computer science, such as the word-problem in theoretical cryptography and the graph-isomorphism problem. In ancient days, mathematicians worked on the solution of linear equations and linear systems. For example, Hero of Alexandria published a book on solving linear equations (Diophantus)–see The Algebraic Work of Hero of Alexandria

The text is written for all students with a basic knowledge of linear algebra, who need to master the modern ideas and methods of applications of linear algebra in areas other than mathematics.