This book helps students to master the material of a standard US undergraduate first course in Linear Algebra. The material is standard in that. This book is meant to provide an introduction to vectors, matrices, and least squares methods, basic topics in applied linear algebra. Our goal is to give the. In broad terms, vectors are things you can add and linear functions are functions of vectors that respect vector addition. The goal of this text is to teach you to.
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Linear Algebra, Theory and Applications was written by Dr. Kenneth Kuttler of Information on The Saylor Foundation's Open Textbook Challenge can be found . Print versions of the book (either a physical copy or a PDF version) have . from another excellent textbook, Introduction to Linear Algebra by L.W. Johnson. In most mathematics programs linear algebra comes in the first or second year, definition of a homomorphism, as is the case in other books, but with that.
Evaluation and the Simplest Properties of Determinants 57 , 3. Minors, Cofactors and the Laplace Theorem 64 , 3.
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Determinants and the Volume of a Parallelepiped in a Euclidean Space 70 , 3. Terminology and General Notes 82 , 4. The Rank of a Matrix 83 , 4. Planes in a Linear Space 87 , 4. Planes in a Euclidean Space 90 , 4. Homogeneous Systems of Linear Equations 93 , 4.
Terminology and General Notes ,85 5. Linear Operations over Operators , 5.
A First Course in Linear Algebra
Multiplication of Operators , 5. Operations over Matrices , 5. The Inverse of a Matrix , 5. Linear Algebra. Commutative Algebra.
Complex Algebra. Elliptic Curves.
Geometric Algebra. Groups Theory. Higher Algebra.
Homological Algebra. Lie Algebra. Differential Algebra. Rings and Fileds. Algebraic Geometry. Differential Geometry.
Conditions of Use
Riemannian Geometry. Mathematical Analysis.
Complex Analysis. Functional Analysis. Differential Analysis.
Fourier Analysis. Harmonic Analysis. Numerical Analysis. Real Analysis.
Algebraic Topology. Differential Topology. Geometric Topology.
Introduction to Linear Algebra, Fifth Edition (2016)
Applied Mathematics. Differential Equations. Discrete Mathematics.
Graph Theory. Number Theory. Probability Theory. Set Theory. Category Theory. Basic Mathematics. Classical Analysis. Modularity rating: 5 The text is written in nice bite-size portions--as the author notes, the material in each section can be covered in about an hour. I teach a 2-credit, very introductory, Intro to Linear Algebra course so I started by reading through only the sections I would cover in that course, and I found that that didn't present much disruption to the flow.
I like the way that examples require the reader to click on their titles, so that the titles serve to break up the "wall of text" while the amount of information presented initially isn't overwhelming. The given organization of topics is clear and logical.
The idiosyncratic chapter naming convention does make navigating via hyperlinks a little confusing, though. Interface rating: 5 There weren't any navigation issues or problems with distracting display features.Linear Dependence 20 , 1. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. It provides an introduction to various numerical methods used in linear algebra.
The first few section of the book, , are essential. Then we would only need the changes between frames -- hopefully small. Orthogonal Complement, Orthogonal Sums of Subspaces 42 , 2.
The text is arranged in such a way that updates would be easy to add. Algebraic Curves. Math has a great flexibility when it comes to being culturally relevant.
Therefore, in sections where methods which are inefficient or unstable for large matrices, major warning signs need to be given.