[PDF] Linear Algebra

What is Linear Algebra? But lets think carefully; what is the left hand side of this equation doing? Functions and equations are different mathematical objects so

LINEAR ALGEBRA KENNETH HOFFMAN Professor of Mathematics Massachusetts Institute of Technology RAY KUNZE Professor of Mathematics University

[PDF] FUNDAMENTALS OF LINEAR ALGEBRA - UBC Math

linear algebra: matrices, linear systems, Gaussian elimination, inverses of matrices and the LDU decomposition In this material, we manage to define the notion

[PDF] Introduction to Applied Linear Algebra - Stanford University

Applied Linear Algebra Vectors, Matrices, and Least Squares Stephen Boyd Department of Electrical Engineering Stanford University Lieven Vandenberghe

[PDF] Lecture notes on linear algebra - Department of Mathematics

These are lecture notes for a first course in linear algebra; the prerequisite is a good course in calculus The notes are quite informal; although I've tried to be

[PDF] Introduction to Linear Algebra - Graduate School of Mathematics

Product 10 - 15 · Lang, Serge, 1927- Introduction to linear algebra (Undergraduate texts in mathematics) Includes index 1 Algebras, Linear I Title II Series

[PDF] Schaums Outline of Linear Algebra (4th Edition)

Seymour Lipschutz, Ph D Marc Lars Lipson, Ph D ISBN: 978-0-07-154353- 8 MHID: 0-07-154353-8 The material in this eBook also appears in the print version

[PDF] álgebra linear

3 sept 2015 · são de que a Álgebra Linear trata simplesmente de álgebra de matrizes reais, para que de imediato fique claro que espaços vetoriais não são

[PDF] Linear Algebra

In most mathematics programs linear algebra comes in the first or second year, following or user's manual would obviously detail the exact syntax needed)

[PDF] algèbre 1 cours pdf

[PDF] algebre 1ere année

[PDF] algebre 2 exercice corrigé

[PDF] algebre 2 exercice corrigé pdf

[PDF] algebre 2 exercices corrigés pdf

[PDF] algebre 2 exo7

[PDF] algebre 3 cours pdf

[PDF] algebre 3 exercices corrigés pdf

[PDF] algebre 3 exo7

[PDF] algebre 4 exercice corrigé

[PDF] algèbre bilinéaire cours et exercices corrigés pdf

[PDF] algèbre bilinéaire forme quadratique

[PDF] algebre exercice

[PDF] algèbre exercices

[PDF] algèbre exercices avec solutions

Linear Algebra

David Cherney, Tom Denton,

Rohit Thomas and Andrew Waldron

Edited by Katrina Glaeser and Travis Scrimshaw

First Edition. Davis California, 2013.This work is licensed under a

Creative Commons Attribution-NonCommercial-

ShareAlike 3.0 Unported License.

1 What is Linear Algebra?

1.1 Organizing Information

1.2 What are Vectors?

1.3 What are Linear Functions?

1.4 So, What is a Matrix?

1.4.1 Matrix Multiplication is Composition of Functions

1.4.2 The Matrix Detour

1.5 Review Problems

2 Systems of Linear Equations

2.1 Gaussian Elimination

2.1.1 Augmented Matrix Notation

2.1.2 Equivalence and the Act of Solving

2.1.3 Reduced Row Echelon Form

2.1.4 Solution Sets and RREF

2.2 Review Problems

2.3 Elementary Row Operations

2.3.1 EROs and Matrices

2.3.2 Recording EROs in (MjI). . . . . . . . . . . . . . . . 54

2.3.3 The Three Elementary Matrices

2.3.4LU,LDU, andPLDUFactorizations. . . . . . . . . . 58

2.4 Review Problems

61
3 4

2.5 Solution Sets for Systems of Linear Equations

2.5.1 The Geometry of Solution Sets: Hyperplanes

2.5.2 Particular Solution+Homogeneous Solutions

2.5.3 Solutions and Linearity

2.6 Review Problems

3 The Simplex Method

3.1 Pablo's Problem

3.2 Graphical Solutions

3.3 Dantzig's Algorithm

3.4 Pablo Meets Dantzig

3.5 Review Problems

4 Vectors in Space,n-Vectors83

4.1 Addition and Scalar Multiplication inRn. . . . . . . . . . . .84

4.2 Hyperplanes

4.3 Directions and Magnitudes

4.4 Vectors, Lists and Functions:RS. . . . . . . . . . . . . . . .94

4.5 Review Problems

5 Vector Spaces

101

5.1 Examples of Vector Spaces

102

5.1.1 Non-Examples

106

5.2 Other Fields

107

5.3 Review Problems

109

6 Linear Transformations

111

6.1 The Consequence of Linearity

112

6.2 Linear Functions on Hyperplanes

114

6.3 Linear Dierential Operators

115

6.4 Bases (Take 1)

115

6.5 Review Problems

118

7 Matrices

121

7.1 Linear Transformations and Matrices

121

7.1.1 Basis Notation

121

7.1.2 From Linear Operators to Matrices

127

7.2 Review Problems

129
4 5

7.3 Properties of Matrices

133

7.3.1 Associativity and Non-Commutativity

140

7.3.2 Block Matrices

142

7.3.3 The Algebra of Square Matrices

143

7.3.4 Trace

145

7.4 Review Problems

146

7.5 Inverse Matrix

150

7.5.1 Three Properties of the Inverse

150

7.5.2 Finding Inverses (Redux)

151

7.5.3 Linear Systems and Inverses

153

7.5.4 Homogeneous Systems

154

7.5.5 Bit Matrices

154

7.6 Review Problems

155

7.7 LU Redux

159

7.7.1 UsingLUDecomposition to Solve Linear Systems. . . 160

7.7.2 Finding anLUDecomposition.. . . . . . . . . . . . . 162

7.7.3 BlockLDUDecomposition. . . . . . . . . . . . . . . . 165

7.8 Review Problems

166

8 Determinants

169

8.1 The Determinant Formula

169

8.1.1 Simple Examples

169

8.1.2 Permutations

170

8.2 Elementary Matrices and Determinants

174

8.2.1 Row Swap

175

8.2.2 Row Multiplication

176

8.2.3 Row Addition

177

8.2.4 Determinant of Products

179

8.3 Review Problems

182

8.4 Properties of the Determinant

186

8.4.1 Determinant of the Inverse

190

8.4.2 Adjoint of a Matrix

190

8.4.3 Application: Volume of a Parallelepiped

192

8.5 Review Problems

193

9 Subspaces and Spanning Sets

195

9.1 Subspaces

195

9.2 Building Subspaces

197
5 6

9.3 Review Problems

202

10 Linear Independence

203

10.1 Showing Linear Dependence

204

10.2 Showing Linear Independence

207

10.3 From Dependent Independent

209

10.4 Review Problems

210

11 Basis and Dimension

213

11.1 Bases inRn.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

11.2 Matrix of a Linear Transformation (Redux)

218

11.3 Review Problems

221

12 Eigenvalues and Eigenvectors

225

12.1 Invariant Directions

227

12.2 The Eigenvalue{Eigenvector Equation

233

12.3 Eigenspaces

236

12.4 Review Problems

238

13 Diagonalization

241

13.1 Diagonalizability

241

13.2 Change of Basis

242

13.3 Changing to a Basis of Eigenvectors

246

13.4 Review Problems

248

14 Orthonormal Bases and Complements

253

14.1 Properties of the Standard Basis

253

14.2 Orthogonal and Orthonormal Bases

255

14.2.1 Orthonormal Bases and Dot Products

256

14.3 Relating Orthonormal Bases

258

14.4 Gram-Schmidt & Orthogonal Complements

quotesdbs_dbs48.pdfusesText_48

[PDF] [PDF] Linear Algebra - UC Davis Mathematics