Dr. J.S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published a number of papers about number theory. For hobbies, he likes to travel and hike, the reason he accepted the position at Brigham Young University.

• PrefaceAdvice to the Reader1 Preliminaries What is Linear Algebra?Rudimentary Set TheoryCartesian ProductsRelationsConcept of a FunctionComposite FunctionsFields of ScalarsTechniques for Proving Theorems2 Matrix Algebra Matrix OperationsGeometric Meaning of a Matrix EquationSystems of Linear EquationInverse of a MatrixThe Equation Ax=bBasic Applications3 Vector Spaces The Concept of a Vector SpaceSubspacesThe Dimension of a Vector SpaceLinear IndependenceApplication of Knowing dim (V)CoordinatesRank of a Matrix4 Linear Maps Linear MapsProperties of Linear MapsMatrix of a Linear MapMatrix Algebra and Algebra of Linear MapsLinear Functionals and DualityEquivalence and SimilarityApplication to Higher Order Differential Equations5 Determinants MotivationProperties of DeterminantsExistence and Uniqueness of DeterminantComputational Definition of DeterminantEvaluation of DeterminantsAdjoint and Cramer's Rule6 Diagonalization MotivationEigenvalues and EigenvectorsCayley-Hamilton Theorem7 Inner Product Spaces Inner ProductFourier SeriesOrthogonal and Orthonormal SetsGram-Schmidt ProcessOrthogonal Projections on Subspaces8 Linear Algebra over Complex Numbers Algebra of Complex NumbersDiagonalization of Matrices with Complex EigenvaluesMatrices over Complex Numbers9 Orthonormal DiagonalizationMotivational IntroductionMatrix Representation of a Quadratic FormSpectral DecompostionConstrained Optimization-Extrema of SpectrumSingular Value Decomposition (SVD)10 Selected Applications of Linear Algebra System of First Order Linear Differential EquationsMultivariable CalculusSpecial Theory of RelativityCryptographySolving Famous Problems from Greek GeometryAnswers to Selected Numberical ProblemsBibliographyIndex

Dr. J.S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published a number of papers about number theory. For hobbies, he likes to travel and hike, the reason he accepted the position at Brigham Young University.

• PrefaceAdvice to the Reader1 Preliminaries What is Linear Algebra?Rudimentary Set TheoryCartesian ProductsRelationsConcept of a FunctionComposite FunctionsFields of ScalarsTechniques for Proving Theorems2 Matrix Algebra Matrix OperationsGeometric Meaning of a Matrix EquationSystems of Linear EquationInverse of a MatrixThe Equation Ax=bBasic Applications3 Vector Spaces The Concept of a Vector SpaceSubspacesThe Dimension of a Vector SpaceLinear IndependenceApplication of Knowing dim (V)CoordinatesRank of a Matrix4 Linear Maps Linear MapsProperties of Linear MapsMatrix of a Linear MapMatrix Algebra and Algebra of Linear MapsLinear Functionals and DualityEquivalence and SimilarityApplication to Higher Order Differential Equations5 Determinants MotivationProperties of DeterminantsExistence and Uniqueness of DeterminantComputational Definition of DeterminantEvaluation of DeterminantsAdjoint and Cramer's Rule6 Diagonalization MotivationEigenvalues and EigenvectorsCayley-Hamilton Theorem7 Inner Product Spaces Inner ProductFourier SeriesOrthogonal and Orthonormal SetsGram-Schmidt ProcessOrthogonal Projections on Subspaces8 Linear Algebra over Complex Numbers Algebra of Complex NumbersDiagonalization of Matrices with Complex EigenvaluesMatrices over Complex Numbers9 Orthonormal DiagonalizationMotivational IntroductionMatrix Representation of a Quadratic FormSpectral DecompostionConstrained Optimization-Extrema of SpectrumSingular Value Decomposition (SVD)10 Selected Applications of Linear Algebra System of First Order Linear Differential EquationsMultivariable CalculusSpecial Theory of RelativityCryptographySolving Famous Problems from Greek GeometryAnswers to Selected Numberical ProblemsBibliographyIndex