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The Resource Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)
Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)
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The item Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 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 selfcontained, 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
 Language

 eng
 eng
 Extent
 1 online resource (561 p.)
 Note
 Description based upon print version of record
 Contents

 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
 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. LUDecomposition; 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. GaussJordan Transformation of a Matrix; 4.4. General Solvability Theorem for Ax = b
 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
 6.4. Matrices with Distinct Eigenvalues6.5. Unitary and Orthogonal Matrices; 6.6. Semidiagonalization Theorem; 6.7. SelfAdjoint 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
 7.8. The Initial Value ProblemProblems; Further Reading; Chapter 8. InfiniteDimensional Linear Vector Spaces; 8.1. Synopsis; 8.2. InfiniteDimensional 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 keterm 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 HilbertSchmidt Operators; 9.4. Volterra Equations
 9.5. Spectral Theory of Integral Operators
 Isbn
 9781281053800
 Label
 Linear algebra and linear operators in engineering with applications in Mathematica
 Title
 Linear algebra and linear operators in engineering with applications in Mathematica
 Statement of responsibility
 H. Ted Davis, Kendall T. Thomson
 Language

 eng
 eng
 Summary
 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 selfcontained, 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
 Cataloging source
 MiAaPQ
 http://library.link/vocab/creatorName
 Davis, H. Ted
 Dewey number

 512.5
 512.502466
 512/.5 21
 Illustrations
 illustrations
 Index
 index present
 Language note
 English
 LC call number
 QA184
 LC item number
 .D38 2000
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Thomson, Kendall T
 Series statement
 Process systems engineering
 Series volume
 v. 3
 http://library.link/vocab/subjectName

 Algebras, Linear
 Linear operators
 Mathematica (Computer program language)
 Label
 Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents

 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
 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. LUDecomposition; 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. GaussJordan Transformation of a Matrix; 4.4. General Solvability Theorem for Ax = b
 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
 6.4. Matrices with Distinct Eigenvalues6.5. Unitary and Orthogonal Matrices; 6.6. Semidiagonalization Theorem; 6.7. SelfAdjoint 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
 7.8. The Initial Value ProblemProblems; Further Reading; Chapter 8. InfiniteDimensional Linear Vector Spaces; 8.1. Synopsis; 8.2. InfiniteDimensional 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 keterm 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 HilbertSchmidt Operators; 9.4. Volterra Equations
 9.5. Spectral Theory of Integral Operators
 Dimensions
 unknown
 Extent
 1 online resource (561 p.)
 Form of item
 online
 Isbn
 9781281053800
 Media category
 computer
 Media type code
 c
 Specific material designation
 remote
 System control number

 (CKB)1000000000383736
 (EBL)313688
 (OCoLC)476103260
 (SSID)ssj0000192586
 (PQKBManifestationID)11196881
 (PQKBTitleCode)TC0000192586
 (PQKBWorkID)10218018
 (PQKB)11764152
 (MiAaPQ)EBC313688
 (EXLCZ)991000000000383736
 Label
 Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents

 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
 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. LUDecomposition; 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. GaussJordan Transformation of a Matrix; 4.4. General Solvability Theorem for Ax = b
 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
 6.4. Matrices with Distinct Eigenvalues6.5. Unitary and Orthogonal Matrices; 6.6. Semidiagonalization Theorem; 6.7. SelfAdjoint 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
 7.8. The Initial Value ProblemProblems; Further Reading; Chapter 8. InfiniteDimensional Linear Vector Spaces; 8.1. Synopsis; 8.2. InfiniteDimensional 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 keterm 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 HilbertSchmidt Operators; 9.4. Volterra Equations
 9.5. Spectral Theory of Integral Operators
 Dimensions
 unknown
 Extent
 1 online resource (561 p.)
 Form of item
 online
 Isbn
 9781281053800
 Media category
 computer
 Media type code
 c
 Specific material designation
 remote
 System control number

 (CKB)1000000000383736
 (EBL)313688
 (OCoLC)476103260
 (SSID)ssj0000192586
 (PQKBManifestationID)11196881
 (PQKBTitleCode)TC0000192586
 (PQKBWorkID)10218018
 (PQKB)11764152
 (MiAaPQ)EBC313688
 (EXLCZ)991000000000383736
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