Finite-dimensional linear algebra. (©2010)

• Record Type: Book
• Further Information: Note: Mark S. Gockenbach.
• Other Names: Gockenbach, Mark S
• Contents: Some Problems Posed on Vector Spaces ; Linear equations; Best approximation; Diagonalization; Summary Fields and Vector Spaces ; Fields; Vector spaces; Subspaces; Linear combinations and spanning sets; Linear independence; Basis and dimension; Properties of bases; Polynomial interpolation and the Lagrange basis; Continuous piecewise polynomial functions Linear Operators; Linear operators; More properties of linear operators; Isomorphic vector spaces; Linear operator equations; Existence and uniqueness of solutions; The fundamental theorem; inverse operators; Gaussian elimination; Newton’s method; Linear ordinary differential equations (ODEs); Graph theory; Coding theory; Linear programming Determinants and Eigenvalues ; The determinant function; Further properties of the determinant function; Practical computation of det(A) ; A note about polynomials; Eigenvalues and the characteristic polynomial; Diagonalization; Eigenvalues of linear operators; Systems of linear ODEs; Integer programming The Jordan Canonical Form ; Invariant subspaces; Generalized eigenspaces; Nilpotent operators; The Jordan canonical form of a matrix; The matrix exponential; Graphs and eigenvalues Orthogonality and Best Approximation ; Norms and inner products; The adjoint of a linear operator; Orthogonal vectors and bases; The projection theorem; The Gram–Schmidt process; Orthogonal complements; Complex inner product spaces; More on polynomial approximation; The energy inner product and Galerkin’s method; Gaussian quadrature; The Helmholtz decomposition The Spectral Theory of Symmetric Matrices ; The spectral theorem for symmetric matrices ; The spectral theorem for normal matrices; Optimization and the Hessian matrix; Lagrange multipliers; Spectral methods for differential equations The Singular Value Decomposition ; Introduction to the singular value decomposition (SVD); The SVD for general matrices; Solving least-squares problems using the SVD; The SVD and linear inverse problems; The Smith normal form of a matrix Matrix Factorizations and Numerical Linear Algebra; The LU factorization; Partial pivoting; The Cholesky factorization; Matrix norms; The sensitivity of linear systems to errors; Numerical stability; The sensitivity of the least-squares problem; The QR factorization; Eigenvalues and simultaneous iteration; The QR algorithm Analysis in Vector Spaces ; Analysis in R n ; Infinite-dimensional vector spaces; Functional analysis; Weak convergence Appendix A: The Euclidean Algorithm; Appendix B: Permutations; Appendix C: Polynomials; Appendix D: Summary of Analysis in R Bibliography Index
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2010
• Copyright Date: 2010
• Extent: 1 online resource (xxi, 650 pages), illustrations
• Subjects: 512.5; Algebras, Linear; Dimensional analysis; Finite fields (Algebra); Vector spaces; Algebras, Linear; Dimensional analysis; Finite fields (Algebra); Vector spaces; Electronic books
• Languages: English
• ISBNs: 9781439882870; 1439882878
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.