A Course in Linear Algebra with Applications
The book is an introduction to Linear Algebra with an account of its principal applications. It is addressed to students of mathematics, the physical, engineering and social sciences, and commerce. The reader is assumed to have completed the calculus sequence. Special features of the book are thorough coverage of all core areas of linear algebra, with a detailed account of such important applications as least squares, systems of linear recurrences, Markov processes, and systems of differential equations. The book also gives an introduction to some more advanced topics such as diagonalization of Hermitian matrices and Jordan form. A principal aim of the book is to make the material accessible to the reader who is not a mathematician, without loss of mathematical rigor. This is reflected in a wealth of examples, the clarity of writing and the organization of material. There is a growing need for knowledge of linear algebra that goes beyond the basic skills of solving systems of linear equations and this book is intended to meet it.
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Chapter One Matrix Algebra
Chapter Two Systems of Linear Equations
Chapter Three Determinants
Chapter Four Introduction to Vector Spaces
Chapter Five Basis and Dimension
Chapter Six Linear Transformations
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arbitrary belongs bilinear form characteristic polynomial coefficient matrix column operations column space column vector complex matrix compute coordinate vector corresponding defined dei(A denote det(A determinant diagonal entries diagonal matrix diagonalizable dimension eigenvalues eigenvectors elementary matrices elementary row operations elements equals EXAMPLE EXERCISES field F field of scalars finitely generated vector form a basis Hence inner product space integers invertible matrix isomorphic Jordan normal form least squares solution line segments linear algebra linear combination linear operator linear system linear system AX linear transformation linearly independent minimum polynomial null space number of pivots obtain ordered basis orthogonal matrix orthonormal basis permutation plane Proof properties Prove quadratic form real numbers reduced row echelon represented respect row echelon form row space rows and columns scalar multiplication skew-symmetric solve square matrix standard basis subspace Suppose systems of linear THEOREM unique vector space zero vector