# 3.5 Change of Basis Definida S Let be v ecao 30 de and let E-M AI. fVe

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##### School: Arizona State University

##### Department: Math

##### Course: Applied Linear Algebra

##### Professor: Jon ulrich

##### Term: Fall 2016

##### Tags: Math and Matrices

##### Name: MAT 343 Notes: Changing Basis

##### Description: These notes cover finding the transition matrix when changing basis. Includes numerous examples and definitions.

##### Uploaded: 02/28/2018

** 14 pages**

**Week 1 Notes **

Fall 2016

Jon ulrich

MAT 343

Week 1 Notes covering introduction to applied linear algebra and covering "Chapter 1: Matrices and Systems of Equations"

** 4 pages**

**MAT 343 Chapter 2.1 Notes: The Determinant of a Matrix**

Fall 2016

Jon ulrich

MAT 343

These notes cover how to solve for the determinant of a matrix, including definitions, theorems, and examples. These notes were taken from MAT 343 taught at ASU.

** 12 pages**

**Exam 1 Study Guide**

Fall 2016

Jon ulrich

MAT 343

This study guide is a summary of each section that will be covered in Exam 1 (sections 1.1-1.5 and 2.1-2.2).

** 3 pages**

**MAT 343 Chapter 3 Section 1: Vector Spaces**

Fall 2016

Jon ulrich

MAT 343

These notes cover the definitions of vector spaces and the functions associated with them. Includes examples, axioms, and theorems from this section.

** 4 pages**

**MAT 343 Section 3.3: Linear Independence **

Fall 2016

Jon ulrich

MAT 343

These notes cover dependency relations and how to show if vectors are linearly independent or dependent. Includes important theorems, observations, and multiple examples.

** 6 pages**

**MAT 343: Study Guide 1 **

Fall 2016

Jon ulrich

MAT 343

These notes cover the material that will be tested on Exam 1. In particular this is the worked out solutions for the practice exam, with highlighted formulas and written notes that explain the process of solving the problems. Hope they help.

** 2 pages**

**Chapter 6.1: Eigenvalues and Eigenvectors**

Fall 2016

Jon ulrich

MAT 343

These notes include definitions and examples of eigenvalues and eigenvectors.

** 2 pages**

**6.3 Diagonalization**

Fall 2016

Jon ulrich

MAT 343

These notes include the theorems and definitions associated with diagonalization. Also includes examples of worked out problems.

** 2 pages**

**MAT 343 Study Guide 2: For Exam on 4/11**

Fall 2016

Jon ulrich

MAT 343

This study guide covers the review problems for the second exam. Each problem is worked out and answered.

** 2 pages**

**MAT 343: Least Squares Problems**

Fall 2016

Jon ulrich

MAT 343

These notes cover the definition of the least squares solution to a problem, and includes examples and theorems associated with them.

** 2 pages**

**Singular Value Decomposition **

Fall 2016

Jon ulrich

MAT 343

These notes cover the definitions and theories associated with singular value decomposition. Also includes examples.

** 3 pages**

**MAT 343 Final Exam Review**

Fall 2016

Jon ulrich

MAT 343

These notes cover the final exam review from class. All problems are worked through and answered, with explanations and step by step completion.

** 14 pages**

**Week 1 Notes **

Fall 2016

Jon ulrich

MAT 343

Week 1 Notes covering introduction to applied linear algebra and covering "Chapter 1: Matrices and Systems of Equations"

** 4 pages**

**MAT 343 Chapter 2.1 Notes: The Determinant of a Matrix**

Fall 2016

Jon ulrich

MAT 343

These notes cover how to solve for the determinant of a matrix, including definitions, theorems, and examples. These notes were taken from MAT 343 taught at ASU.

** 12 pages**

**Exam 1 Study Guide**

Fall 2016

Jon ulrich

MAT 343

This study guide is a summary of each section that will be covered in Exam 1 (sections 1.1-1.5 and 2.1-2.2).

** 3 pages**

**MAT 343 Chapter 3 Section 1: Vector Spaces**

Fall 2016

Jon ulrich

MAT 343

These notes cover the definitions of vector spaces and the functions associated with them. Includes examples, axioms, and theorems from this section.

** 4 pages**

**MAT 343 Section 3.3: Linear Independence **

Fall 2016

Jon ulrich

MAT 343

These notes cover dependency relations and how to show if vectors are linearly independent or dependent. Includes important theorems, observations, and multiple examples.

** 6 pages**

**MAT 343: Study Guide 1 **

Fall 2016

Jon ulrich

MAT 343

These notes cover the material that will be tested on Exam 1. In particular this is the worked out solutions for the practice exam, with highlighted formulas and written notes that explain the process of solving the problems. Hope they help.

** 2 pages**

**Chapter 6.1: Eigenvalues and Eigenvectors**

Fall 2016

Jon ulrich

MAT 343

These notes include definitions and examples of eigenvalues and eigenvectors.

** 2 pages**

**6.3 Diagonalization**

Fall 2016

Jon ulrich

MAT 343

These notes include the theorems and definitions associated with diagonalization. Also includes examples of worked out problems.

** 2 pages**

**MAT 343 Study Guide 2: For Exam on 4/11**

Fall 2016

Jon ulrich

MAT 343

This study guide covers the review problems for the second exam. Each problem is worked out and answered.

** 2 pages**

**MAT 343: Least Squares Problems**

Fall 2016

Jon ulrich

MAT 343

These notes cover the definition of the least squares solution to a problem, and includes examples and theorems associated with them.

** 2 pages**

**Singular Value Decomposition **

Fall 2016

Jon ulrich

MAT 343

These notes cover the definitions and theories associated with singular value decomposition. Also includes examples.

** 3 pages**

**MAT 343 Final Exam Review**

Fall 2016

Jon ulrich

MAT 343

These notes cover the final exam review from class. All problems are worked through and answered, with explanations and step by step completion.

** 3 pages**

**MAT 343 Chapter 3 Section 1: Vector Spaces**

Fall 2016

Jon ulrich

MAT 343

These notes cover the definitions of vector spaces and the functions associated with them. Includes examples, axioms, and theorems from this section.

** 2 pages**

**Chapter 6.1: Eigenvalues and Eigenvectors**

Fall 2016

Jon ulrich

MAT 343

These notes include definitions and examples of eigenvalues and eigenvectors.

** 14 pages**

**Week 1 Notes **

Fall 2016

Jon ulrich

MAT 343

Week 1 Notes covering introduction to applied linear algebra and covering "Chapter 1: Matrices and Systems of Equations"

** 2 pages**

**MAT 343: Least Squares Problems**

Fall 2016

Jon ulrich

MAT 343

These notes cover the definition of the least squares solution to a problem, and includes examples and theorems associated with them.

** 2 pages**

**6.3 Diagonalization**

Fall 2016

Jon ulrich

MAT 343

These notes include the theorems and definitions associated with diagonalization. Also includes examples of worked out problems.

** 4 pages**

**MAT 343 Chapter 2.1 Notes: The Determinant of a Matrix**

Fall 2016

Jon ulrich

MAT 343

These notes cover how to solve for the determinant of a matrix, including definitions, theorems, and examples. These notes were taken from MAT 343 taught at ASU.

** 4 pages**

**MAT 343 Section 3.3: Linear Independence **

Fall 2016

Jon ulrich

MAT 343

These notes cover dependency relations and how to show if vectors are linearly independent or dependent. Includes important theorems, observations, and multiple examples.

** 2 pages**

**Singular Value Decomposition **

Fall 2016

Jon ulrich

MAT 343

These notes cover the definitions and theories associated with singular value decomposition. Also includes examples.

** 6 pages**

**MAT 343: Study Guide 1 **

Fall 2016

Jon ulrich

MAT 343

These notes cover the material that will be tested on Exam 1. In particular this is the worked out solutions for the practice exam, with highlighted formulas and written notes that explain the process of solving the problems. Hope they help.

** 3 pages**

**MAT 343 Final Exam Review**

Fall 2016

Jon ulrich

MAT 343

These notes cover the final exam review from class. All problems are worked through and answered, with explanations and step by step completion.

** 12 pages**

**Exam 1 Study Guide**

Fall 2016

Jon ulrich

MAT 343

This study guide is a summary of each section that will be covered in Exam 1 (sections 1.1-1.5 and 2.1-2.2).

** 2 pages**

**MAT 343 Study Guide 2: For Exam on 4/11**

Fall 2016

Jon ulrich

MAT 343

This study guide covers the review problems for the second exam. Each problem is worked out and answered.