Elementary Linear Algebra 1st Edition by James Kirkwood, Bessie Kirkwood 1351253109 9781351253109

Elementary Linear Algebra 1st Edition by James R. Kirkwood, Bessie H. Kirkwood – Ebook PDF Instant Download/DeliveryISBN:  1351253109, 9781351253109  

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ISBN-10 ‏ : ‎1351253109 

ISBN-13 ‏ : ‎ 9781351253109

Author: James R. Kirkwood, Bessie H. Kirkwood 

Elementary Linear Algebra is written for the first undergraduate course. The book focuses on the importance of linear algebra in many disciplines such as engineering, economics, statistics, and computer science. The text reinforces critical ideas and lessons of traditional topics. More importantly, the book is written in a manner that deeply ingrains computational methods.

Elementary Linear Algebra 1st Table of contents:

1. Matrices
1.1 Matrix Arithmetic
1.1.1 Matrix Arithmetic
1.1.1.1 Matrix Addition
1.1.1.2 Scalar Multiplication
1.1.1.3 Matrix Multiplication
Exercises
1.2 The Algebra of Matrices
1.2.1 Properties of Matrix Addition, Scalar Multiplication, and Matrix Multiplication
1.2.2 The Identity Matrix
1.2.3 The Inverse of a Square Matrix
1.2.4 Determinants
1.2.5 Elementary Matrices
1.2.6 Matrices That Interchange Two Rows of a Matrix
1.2.7 Multiplying a Row of a Matrix by a Constant
1.2.8 Adding a Multiple of One Row to Another Row
1.2.9 Computing the Inverse of a Matrix
1.2.10 The Transpose of a Matrix
Exercises
1.3 The LU Decomposition of a Square Matrix (Optional)
Exercises
2. Systems of Linear Equations
2.1 Basic Definitions
Exercises
2.2 Solving Systems of Linear Equations (Gaussian Elimination)
2.2.1 Solving Systems of Linear Equations
2.2.2 Using Technology to Accomplish Gaussian Elimination
Exercises
2.3 Equivalent Systems of Linear Equations
2.3.1 Row Reduced Form of a Matrix
Exercises
2.4 Expressing the Solution of a System of Linear Equations
2.4.1 Systems of Linear Equations That Have No Solutions
2.4.2 Systems of Linear Equations That Have Exactly One Solution
2.4.3 Systems of Linear Equations That Have Infinitely Many Solutions
2.4.4 Application of Linear Systems to Curve Fitting
Exercises
2.5 Expressing Systems of Linear Equations in Other Forms
2.5.1 Representing a System of Linear Equations as a Vector Equation
2.5.2 Equivalence of a System of Linear Equations and a Matrix Equation
Exercises
2.6 Applications
2.6.1 Flow Problems
2.6.2 Example: Kirchoff’s Laws
2.6.3 Balancing Chemical Equations Using Linear Algebra
Exercises
2.6.4 Markov Chains
Exercises
3. Vector Spaces
3.1 Vector Spaces in ℝn
Exercises
3.2 Axioms and Examples of Vector Spaces
3.2.1 Some Examples of Sets That Are Not Vector Spaces
3.2.2 Additional Properties of Vector Spaces
Exercises
3.3 Subspaces of a Vector Space
Exercises
3.4 Spanning Sets, Linearly Independent Sets and Bases
Exercises
3.5 Converting a Set of Vectors to a Basis
3.6 A Synopsis of Sections 3.3.4 and 3.3.5
Exercises
3.7 Change of Bases
Exercises
3.8 Null Space, Row Space, and Column Space of a Matrix
Exercises
3.9 Sums and Direct Sums of Vector Spaces (Optional)
Exercises
4. Linear Transformations
4.1 Properties of a Linear Transformation
4.1.1 Null Space and Range (Image) of a Linear Transformation
Exercises
4.2 Representing a Linear Transformation
4.2.1 Representation of a Linear Transformation in the Usual Basis
Exercises
4.3 Finding the Representation of a Linear Operator with respect to Different Bases
Exercises
4.4 Composition (Multiplication) of Linear Transformations
Exercises
5. Eigenvalues and Eigenvectors
5.1 Determining Eigenvalues and Eigenvectors
5.1.1 Finding the Eigenvectors after the Eigenvalues Have Been Found
Exercises
5.2 Diagonalizing a Matrix
5.2.1 Algebraic and Geometric Multiplicities of an Eigenvalue
5.2.2 Diagonalizing a Matrix
Exercises
5.3 Similar Matrices
Exercises
5.4 Eigenvalues and Eigenvectors in Systems of Differential Equations
Exercises
6. Inner Product Spaces
6.1 Some Facts about Complex Numbers
Exercises
6.2 Inner Product Spaces
Exercises
6.3 Orthogonality
Exercises
6.4 The Gram–Schmidt Process
6.4.1 Algorithm for the Gram–Schmidt Process
Exercises
6.5 Representation of a Linear Transformation on Inner Product Spaces (Optional)
Exercises
6.6 Orthogonal Complement
Exercises
6.7 Four Subspaces Associated with a Matrix (Optional)
6.8 Projections
Exercises
6.9 Least-Squares Estimates in Statistics (Optional)
Exercise
6.10 Weighted Inner Products (Optional)
Reference
7. Linear Functionals, Dual Spaces, and Adjoint Operators
7.1 Linear Functionals
7.1.1 The Second Dual of a Vector Space (Optional)
Exercises
7.2 The Adjoint of a Linear Operator
7.2.1 The Adjoint Operator
7.2.2 Adjoint on Weighted Inner Product Spaces (Optional)
Exercises
7.3 The Spectral Theorem

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Tags: Elementary, Linear Algebra, James Kirkwood, Bessie Kirkwood