000			04059nam a2200361 4500
001			OTLid0000213
003			MnU
005			20201105133307.0
006			m o d s
008			180907s2017 mnu o 0 0 eng d
020			_a
040			_aMnU _beng _cMnU
050		4	_aQA1
050		4	_aQA37.3
100	1		_aKuttler, Ken _eauthor
245	0	2	_aA First Course in Linear Algebra _cKen Kuttler
264		2	_bOpen Textbook Library
264		1	_bLyryx
300			_a1 online resource
490	0		_aOpen textbook library.
505	0		_a1 Systems of Equations -- 1.1 Systems of Equations, Geometry -- 1.2 Systems Of Equations, Algebraic Procedures -- 2 Matrices -- 2.1 Matrix Arithmetic -- 2.2 LU Factorization -- 3 Determinants -- 3.1 Basic Techniques and Properties -- 3.2 Applications of the Determinant -- 4 R^n -- 4.1 Vectors in R^n -- 4.2 Algebra in R^n -- 4.3 Geometric Meaning of Vector Addition -- 4.4 Length of a Vector -- 4.5 Geometric Meaning of Scalar Multiplication -- 4.6 Parametric Lines -- 4.7 The Dot Product -- 4.8 Planes in R^n -- 4.9 The Cross Product -- 4.10 Spanning, Linear Independence and Basis in R^n -- 4.11 Orthogonality and the Gram Schmidt Process -- 4.12 Applications -- 5 Linear Transformations -- 5.1 Linear Transformations -- 5.2 The Matrix of a Linear Transformation I -- 5.3 Properties of Linear Transformations -- 5.4 Special Linear Transformations in R^2 -- 5.5 One to One and Onto Transformations -- 5.6 Isomorphisms -- 5.7 The Kernel And Image Of A Linear Map -- 5.8 The Matrix of a Linear Transformation II -- 5.9 The General Solution of a Linear System -- 6 Complex Numbers -- 6.1 Complex Numbers -- 6.2 Polar Form -- 6.3 Roots of Complex Numbers -- 6.4 The Quadratic Formula -- 7 Spectral Theory -- 7.1 Eigenvalues and Eigenvectors of a Matrix -- 7.2 Diagonalization -- 7.3 Applications of Spectral Theory -- 7.4 Orthogonality -- 8 Some Curvilinear Coordinate Systems -- 8.1 Polar Coordinates and Polar Graphs -- 8.2 Spherical and Cylindrical Coordinates -- 9 Vector Spaces -- 9.1 Algebraic Considerations -- 9.2 Spanning Sets -- 9.3 Linear Independence -- 9.4 Subspaces and Basis -- 9.5 Sums and Intersections -- 9.6 Linear Transformations -- 9.7 Isomorphisms -- 9.8 The Kernel And Image Of A Linear Map -- 9.9 The Matrix of a Linear Transformation -- A Some Prerequisite Topics -- A.1 Sets and Set Notation -- A.2 Well Ordering and Induction -- B Selected Exercise Answers
520	0		_aThis text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
542	1		_fAttribution
546			_aIn English.
588	0		_aDescription based on print resource
650		0	_aMathematics _vTextbooks
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/213 _zAccess online version
999			_c19619 _d19619