A Course in Linear AlgebraSuitable for advanced undergraduates and graduate students, this text offers a complete introduction to the basic concepts of linear algebra. Interesting and inspiring in its approach, it imparts an understanding of the subject's logical structure as well as the ways in which linear algebra provides solutions to problems in many branches of mathematics. The authors define general vector spaces and linear mappings at the outset and base all subsequent developments on these concepts. This approach provides a ready-made context, motivation, and geometric interpretation for each new computational technique. Proofs and abstract problem-solving are introduced from the start, offering students an immediate opportunity to practice applying what they've learned. Each chapter contains an introduction, summary, and supplementary exercises. The text concludes with a pair of helpful appendixes and solutions to selected exercises. |
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a₁ a₂ b₁ calculation canonical basis Chapter characteristic polynomial coefficients complex numbers compute consider coordinate vector Corollary defined Definition denoted det(A determinant diagonal entries diagonalizable differential equations dim(Ker(T dim(V dim(W dimension distinct eigenvalues e₁ eigenspace eigenvalues eigenvectors Example Exercise finite finite-dimensional vector space free variables geometric Hence Hermitian inner product Im(T induction injective integer invertible isomorphism Jordan canonical form Jordan form Ker(T linear algebra linear combination linear equations linear mapping linear transformation linearly independent mathematics minimal polynomial nilpotent nonzero obtain operations orthogonal projection orthonormal basis proof properties Proposition Prove real numbers result roots satisfies scalar multiplication Section set of solutions set of vectors Show solving Span(S spectral theorem standard basis statement subset subspace surjective symmetric symmetric matrix system of equations system of linear unique V₁ V₂ W₁ W₂ x₁ y₁ zero