Linear algebra done rightThis text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presentswithout having defined determinantsa clean proof that every linear operator on a finitedimensional complex vector space (or an odddimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus, the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to innerproduct spaces in the first half of the book and shortly thereafter to the finitedimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on selfadjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text. 
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Review: Linear Algebra Done Right
User Review  Daniel  GoodreadsThe title says it all. Read full review
Review: Linear Algebra Done Right
User Review  Justin  GoodreadsThis book was a real pageturner! Great approach towards linear algebra. Sheldon Axler doesn't introduce determinants until the end, which was a true delight in my opinion because it surely kept me ... Read full review
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a e F additive identity additive inverse adjoint block uppertriangular matrix chapter characteristic polynomial completing the proof complex innerproduct space complex numbers complex vector space compute consisting of eigenvectors coordinates corollary corresponding decomposition definition denote dimension dimensional dimV direct sum eigenpair eigenvalues elements of F entries equation example exists finite finitedimensional vector space function hence implies injective invariant subspaces invertible isometry length linear algebra linear combination linear map linearly independent tuple matrix with respect minimal polynomial ntuple nilpotent nonzero vector Note null space orthogonal orthonormal basis orthonormal tuple permutation positive integer positive operator Prove real innerproduct space real numbers real vector space right side scalar multiplication selfadjoint operator space over F span(vi spanning tuple spectral theorem square matrix square root subset Suppose surjective tuple of vectors unique verify vT*T words z e F