UID:
almahu_9949697605602882
Umfang:
1 online resource (561 p.)
ISBN:
1-281-05380-5
,
9786611053802
,
0-08-051024-8
Serie:
Process systems engineering ; v. 3
Inhalt:
Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert sp
Anmerkung:
Description based upon print version of record.
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Cover; Linear Algebra and Linear Operators in Engineering; Copyright Page; Contents; Preface; Chapter 1. Determinants; 1.1. Synopsis; 1.2. Matrices; 1.3. Definition of a Determinant; 1.4. Elementary Properties of Determinants; 1.5. Cofactor Expansions; 1.6. Cramer's Rule for Linear Equations; 1.7. Minors and Rank of Matrices; Problems; Further Reading; Chapter 2. Vectors and Matrices; 2.1. Synopsis; 2.2. Addition and Multiplication; 2.3. The Inverse Matrix; 2.4. Transpose and Adjoint; 2.5. Partitioning Matrices; 2.6. Linear Vector Spaces; Problems; Further Reading
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Chapter 3. Solution of Linear and Nonlinear Systems3.1. Synopsis; 3.2. Simple Gauss Elimination; 3.3. Gauss Elimination with Pivoting; 3.4. Computing the Inverse of a Matrix; 3.5. LU-Decomposition; 3.6. Band Matrices; 3.7. Iterative Methods for Solving Ax = b; 3.8. Nonhnear Equations; Problems; Further Reading; Chapter 4. General Theory of Solvability of Linear Algebraic Equations; 4.1. Synopsis; 4.2. Sylvester's Theorem and the Determinants of Matrix Products; 4.3. Gauss-Jordan Transformation of a Matrix; 4.4. General Solvability Theorem for Ax = b
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4.5. Linear Dependence of a Vector Set and the Rank of Its Matrix4.6. The Fredholm Alternative Theorem; Problems; Further Reading; Chapter 5. The Eigenproblem; 5.1. Synopsis; 5.2. Linear Operators in a Normed Linear Vector Space; 5.3. Basis Sets in a Normed Linear Vector Space; 5.4. Eigenvalue Analysis; 5.5. Some Special Properties of Eigenvalues; 5.6. Calculation of Eigenvalues; Problems; Further Reading; Chapter 6. Perfect Matrices; 6.1. Synopsis; 6.2. Implications of the Spectral Resolution Theorem; 6.3. Diagonalization by a Similarity Transformation
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6.4. Matrices with Distinct Eigenvalues6.5. Unitary and Orthogonal Matrices; 6.6. Semidiagonalization Theorem; 6.7. Self-Adjoint Matrices; 6.8. Normal Matrices; 6.9. Miscellanea; 6.10. The Initial Value Problem; 6.11. Perturbation Theory; Problems; Further Reading; Chapter 7. Imperfect or Defective Matrices; 7.1. Synopsis; 7.2. Rank of the Characteristic Matrix; 7.3. Jordan Block Diagonal Matrices; 7.4. The Jordan Canonical Form; 7.5. Determination of Generalized Eigenvectors; 7.6. Dyadic Form of an Imperfect Matrix; 7.7. Schmidt's Normal Form of an Arbitrary Square Matrix
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7.8. The Initial Value ProblemProblems; Further Reading; Chapter 8. Infinite-Dimensional Linear Vector Spaces; 8.1. Synopsis; 8.2. Infinite-Dimensional Spaces; 8.3. Riemann and Lebesgue Integration; 8.4. Inner Product Spaces; 8.5. Hilbert Spaces; 8.6. Basis Vectors; 8.7. Linear Operators; 8.8. Solutions to Problems Involving ke-term Dyadics; 8.9. Perfect Operators; Problems; Further Reading; Chapter 9. Linear Integral Operators in a Hilbert Space; 9.1. Synopsis; 9.2. Solvability Theorems; 9.3. Completely Continuous and Hilbert-Schmidt Operators; 9.4. Volterra Equations
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9.5. Spectral Theory of Integral Operators
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English
Weitere Ausg.:
ISBN 0-12-206349-X
Sprache:
Englisch
