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Linear Algebra and Matrix Theory Jimmie Gilbert

Linear Algebra and Matrix Theory By Jimmie Gilbert

Linear Algebra and Matrix Theory by Jimmie Gilbert

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Linear Algebra and Matrix Theory Summary

Linear Algebra and Matrix Theory by Jimmie Gilbert

Master linear algebra with LINEAR ALGEBRA AND MATRIX THEORY! With coverage of the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices, this mathematics text prepares you to succeed in this course and in math courses in your future. Numerous examples and exercises illustrate the theories and provide you with the practice you need to master difficult concepts.

Linear Algebra and Matrix Theory Reviews

1. REAL COORDINATE SPACES. The Vector Spaces Rn. Linear Independence. Subspaces of Rn. Spanning Sets. Geometric Interpretations of R^2 and R^3. Bases and Dimension. 2. ELEMENTARY OPERATIONS ON VECTORS. Elementary Operations and Their Inverses. Elementary Operations and Linear Independence. Standard Bases for Subspaces. 3. MATRIX MULTIPLICATION. Matrices of Transition. Properties of Matrix Multiplication. Invertible Matrices. Column Operations and Column-Echelon Forms. Row Operations and Row-Echelon Forms. Row and Column Equivalence. Rank and Equivalence. LU Decompositions. 4. VECTOR SPACES, MATRICES, AND LINEAR EQUATIONS. Vector Spaces. Subspaces and Related Concepts. Isomorphisms of Vector Spaces. Standard Bases for Subspaces. Matrices over an Arbitrary Field. Systems of Linear Equations. More on Systems of Linear Equations. 5. LINEAR TRANSFORMATIONS. Linear Transformations. Linear Transformations and Matrices. Change of Basis. Composition of Linear Transformations. 6. DETERMINANTS. Permutations and Indices. The Definition of a Determinant. Cofactor Expansions. Elementary Operations and Cramer's Rule. Determinants and Matrix Multiplication. 7. EIGENVALUES AND EIGENVECTORS. Eigenvalues and Eigenvectors. Eigenspaces and Similarity. Representation by a Diagonal Matrix. 8. FUNCTIONS OF VECTORS. Linear Functionals. Real Quadratic Forms. Orthogonal Matrices. Reduction of Real Quadratic Forms. Classification of Real Quadratic Forms. Binlinear Forms. Symmetric Bilinear Forms. Hermitian Forms. 9. INNER PRODUCT SPACES. Inner Products. Norms and Distances. Orthonormal Bases. Orthogonal Complements. Isometrics. Normal Matrices. Normal Linear Operators. 10. SPECTRAL DECOMPOSITIONS. Projections and Direct Sums. Spectral Decompositions. Minimal Polynomials and Spectral Decompositions. Nilpotent Transformations. The Jordan Canonical Form. 11. NUMERICAL METHODS. Sequences and Series of Vectors. Sequences and Series of Matrices. The Standard Method of Iteration. Cimmino's Method. An Iterative Method for Determining Eigenvalues.

Table of Contents

1. REAL COORDINATE SPACES. The Vector Spaces Rn. Linear Independence. Subspaces of Rn. Spanning Sets. Geometric Interpretations of R^2 and R^3. Bases and Dimension. 2. ELEMENTARY OPERATIONS ON VECTORS. Elementary Operations and Their Inverses. Elementary Operations and Linear Independence. Standard Bases for Subspaces. 3. MATRIX MULTIPLICATION. Matrices of Transition. Properties of Matrix Multiplication. Invertible Matrices. Column Operations and Column-Echelon Forms. Row Operations and Row-Echelon Forms. Row and Column Equivalence. Rank and Equivalence. LU Decompositions. 4. VECTOR SPACES, MATRICES, AND LINEAR EQUATIONS. Vector Spaces. Subspaces and Related Concepts. Isomorphisms of Vector Spaces. Standard Bases for Subspaces. Matrices over an Arbitrary Field. Systems of Linear Equations. More on Systems of Linear Equations. 5. LINEAR TRANSFORMATIONS. Linear Transformations. Linear Transformations and Matrices. Change of Basis. Composition of Linear Transformations. 6. DETERMINANTS. Permutations and Indices. The Definition of a Determinant. Cofactor Expansions. Elementary Operations and Cramer's Rule. Determinants and Matrix Multiplication. 7. EIGENVALUES AND EIGENVECTORS. Eigenvalues and Eigenvectors. Eigenspaces and Similarity. Representation by a Diagonal Matrix. 8. FUNCTIONS OF VECTORS. Linear Functionals. Real Quadratic Forms. Orthogonal Matrices. Reduction of Real Quadratic Forms. Classification of Real Quadratic Forms. Binlinear Forms. Symmetric Bilinear Forms. Hermitian Forms. 9. INNER PRODUCT SPACES. Inner Products. Norms and Distances. Orthonormal Bases. Orthogonal Complements. Isometrics. Normal Matrices. Normal Linear Operators. 10. SPECTRAL DECOMPOSITIONS. Projections and Direct Sums. Spectral Decompositions. Minimal Polynomials and Spectral Decompositions. Nilpotent Transformations. The Jordan Canonical Form. 11. NUMERICAL METHODS. Sequences and Series of Vectors. Sequences and Series of Matrices. The Standard Method of Iteration. Cimmino's Method. An Iterative Method for Determining Eigenvalues.

Additional information

CIN0534405819G
9780534405816
0534405819
Linear Algebra and Matrix Theory by Jimmie Gilbert
Jimmie Gilbert
Used - Good
Hardback
Cengage Learning, Inc
20040216
544
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

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