Linear Algebra Done Right, Second Edition - UFPE

Linear AlgebraDone Right, Second EditionSheldon AxlerSpringerContentsPreface to the InstructorixPreface to the StudentxiiiAcknowledgmentsxvChapter1 Vector Spaces1 Complex of Vector of Vector and Direct Vector Spaces21 Span and Linear Maps37 Definitions and Spaces and Matrix of a Linear and Eigenvectors75 Invariant Applied to Subspaces on Real Vector Spaces97 Inner Projections and Minimization Functionals and on Inner-Product Spaces127 Self-Adjoint and Normal Spectral Operators on Real Inner-Product and Singular-Value on Complex Vector Spaces163 Generalized Characteristic of an Minimal on Real Vector Spaces193 Eigenvalues of Square Upper-Triangular Characteristic and Determinant213 Change of of an of a Index247 Index249 Preface to the InstructorYou are probably about to teach a course that will give studentstheir Second exposure to Linear Algebra . During their first brush withthe subject, your students probably worked with Euclidean spaces andmatrices.

x Preface to the Instructor •Linear maps are introduced in Chapter 3.The key result here is that for a linear map T, the dimension of the null space of T plus the dimension of the range of Tequals the dimension of the domain of T. •The part of the theory of polynomials that will be needed to un- derstand linear operators is presented in Chapter 4.

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