Linear algebra
Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determ…
Read More ↓Title Statements
- Full title :Linear algebra / Elizabeth S. Meckes, Case Western Reserve University, Cleveland, OH, USA, Mark W. Meckes, Case Western Reserve University, Cleveland, OH, USA.
Summary
Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants. --
Read More ↓Edition Statements
- Publication Date:©2018
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge, United Kingdom
- Language:eng
- Publication Date:©2018
Notes
Includes index.
The Physical Object
- Description:xvi, 427 pages : : illustrations (some color) ; : 26 cm.
Edition Identifiers
- ISBN:9781107177901, 1107177901
- oclc:on1012749835
- LC Classification:QA184.2
- Dewey Decimal:512/.5
Table of Contents
Machine generated contents note: 1.Linear Systems and Vector Spaces -- 1.1.Linear Systems of Equations -- Bread, Beer, and Barley -- Linear Systems and Solutions -- 1.2.Gaussian Elimination -- The Augmented Matrix of a Linear System -- Row Operations -- Does it Always Work? -- Pivots and Existence and Uniqueness of Solutions -- 1.3.Vectors and the Geometry of Linear Systems -- Vectors and Linear Combinations -- The Vector Form of a Linear System -- The Geometry of Linear Combinations -- The Geometry of Solutions -- 1.4.Fields -- General Fields -- Arithmetic in Fields -- Linear Systems over a Field -- 1.5.Vector Spaces -- General Vector Spaces -- Examples of Vector Spaces -- Arithmetic in Vector Spaces -- 2.Linear Maps and Matrices -- 2.1.Linear Maps -- Recognizing Sameness -- Linear Maps in Geometry -- Matrices as Linear Maps -- Eigenvalues and Eigenvectors -- The Matrix -- Vector Form of a Linear System -- 2.2.More on Linear Maps -- Isomorphism -- Properties of Linear Maps
Note continued: The Matrix of a Linear Map -- Some Linear Maps on Function and Sequence Spaces -- 2.3.Matrix Multiplication -- Definition of Matrix Multiplication -- Other Ways of Looking at Matrix Multiplicat…
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