Linear Algebra: Pearson New International Edition (häftad)
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Format
Häftad (Paperback)
Språk
Engelska
Antal sidor
536
Utgivningsdatum
2013-07-23
Upplaga
4
Förlag
Pearson
Medarbetare
Friedberg, Stephen / Insel, Arnold / Spence, Lawrence
Dimensioner
279 x 215 x 23 mm
Vikt
1280 g
Antal komponenter
1
ISBN
9781292026503
Linear Algebra: Pearson New International Edition (häftad)

Linear Algebra: Pearson New International Edition

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Häftad Engelska, 2013-07-23
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For courses in Advanced Linear Algebra.

This top-selling, theorem-proof text presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.
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Innehållsförteckning



1. Vector Spaces.

 

Introduction. Vector Spaces. Subspaces. Linear Combinations and Systems of Linear Equations. Linear Dependence and Linear Independence. Bases and Dimension. Maximal Linearly Independent Subsets.

 



2. Linear Transformations and Matrices.

 

Linear Transformations, Null Spaces, and Ranges. The Matrix Representation of a Linear Transformation. Composition of Linear Transformations and Matrix Multiplication. Invertibility and Isomorphisms. The Change of Coordinate Matrix. Dual Spaces. Homogeneous Linear Differential Equations with Constant Coefficients.

 



3. Elementary Matrix Operations and Systems of Linear Equations.

 

Elementary Matrix Operations and Elementary Matrices. The Rank of a Matrix and Matrix Inverses. Systems of Linear EquationsTheoretical Aspects. Systems of Linear EquationsComputational Aspects.

 



4. Determinants.

 

Determinants of Order 2. Determinants of Order n. Properties of Determinants. SummaryImportant Facts about Determinants. A Characterization of the Determinant.

 



5. Diagonalization.

 

Eigenvalues and Eigenvectors. Diagonalizability. Matrix Limits and Markov Chains. Invariant Subspaces and the Cayley-Hamilton Theorem.

 



6. Inner Product Spaces.

 

Inner Products and Norms. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements. The Adjoint of a Linear Operator. Normal and Self-Adjoint Operators. Unitary and Orthogonal Operators and Their Matrices. Orthogonal Projections and the Spectral Theorem. The Singular Value Decomposition and the Pseudoinverse. Bilinear and Quadratic Forms. Einstein's Special Theory of Relativity. Conditioning and the Rayleigh Quotient. The Geometry of Orthogonal Operators.



Appendices.

 

Sets. Functions. Fields. Complex Numbers. Polynomials.

 



Answers to Selected Exercises.


Index.