Matrix Algebra with Computational Applications (Colbry)
- Page ID
- 63409
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Matrix Algebra with Computational Applications is a collection of Open Educational Resource (OER) materials designed to introduce students to the use of Linear Algebra to solve real world problems. These materials were developed specifically for students and instructors working in a “flipped classroom” model that emphasizes hands-on problem solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom. The materials are organized into a semester long course with “pre-class” and “in-class” assignments. The “pre-class” assignments include readings, video lectures and coding projects (in Python), which students are expected to complete before attending class. The in-class assignments consist of hands-on individual and group activities intended to be completed during class. These in-class activities are supervised by the instructors, who actively answer questions and help guide the students in achieving the learning goals for the course.
To be successful in this course, students need to have strong Python programming skills. Students will leverage these coding skills to write programs that use Linear Algebra to solve science and engineering problems. Although it is important for students to understand the mathematical concepts behind the materials, this course is not intended to teach students how to do mathematical proofs.
- Front Matter
- 1: Matrix Algebra class preparation checklist
- 2: 01 In-Class Assignment - Welcome to Matrix Algebra with computational applications
- 3: 02 Pre-Class Assignment - Vectors
- 4: 02 In-Class Assignment - Vectors
- 5: 03 Pre-Class Assignment - Linear Equations
- 6: 03 In-Class Assignment - Solving Linear Systems of equations
- 7: 04 Pre-Class Assignment - Python Linear Algebra Packages
- 8: 04 In-Class Assignment - Linear Algebra and Python
- 9: 05 Pre-Class Assignment - Gauss-Jordan Elimination
- 10: 05 In-Class Assignment - Gauss-Jordan
- 11: 06 Pre-Class Assignment - Matrix Mechanics
- 12: 06 In-Class Assignment - Matrix Multiply
- 13: 07 Pre-Class Assignment - Transformation Matrix
- 14: 07 In-Class Assignment - Transformations
- 15: 08 Pre-Class Assignment - Robotics and Reference Frames
- 16: 08 In-Class Assignment - The Kinematics of Robotics
- 17: 09 Pre-Class Assignment - Determinants
- 18: 09 In-Class Assignment - Determinants
- 19: 10 Pre-Class Assignment - Eigenvectors and Eigenvalues
- 20: 10 In-Class Assignment - Eigenproblems
- 21: 11 Pre-Class Assignment - Vector Spaces
- 22: 11 In-Class Assignment - Vector Spaces
- 23: 12 Pre-Class Assignment - Matrix Spaces
- 24: 12 In-Class Assignment - Matrix Representation
- 25: 13 Pre-Class Assignment - Projections
- 26: 13 In-Class Assignment - Projections
- 27: 14 Pre-Class Assignment - Fundamental Spaces
- 28: 14 In-Class Assignment - Fundamental Spaces
- 29: 15 Pre-Class Assignment - Diagonalization and Powers
- 30: 15 In-Class Assignment - Diagonalization
- 31: 16 Pre-Class Assignment - Linear Dynamical Systems
- 32: 16 In-Class Assignment - Linear Dynamical Systems
- 33: 17 Pre-Class Assignment - Decompositions
- 34: 17 In-Class Assignment - Decompositions and Gaussian Elimination
- 35: 18 Pre-Class Assignment - Inner Product
- 36: 18 In-Class Assignment - Inner Products
- 37: 19 Pre-Class Assignment - Least Squares Fit (Regression)
- 38: 19 In-Class Assignment - Least Squares Fit (LSF)
- 39: 20 In-Class Assignment - Least Squares Fit (LSF)
- 40: Pre-Class Assignment - Solve Linear Systems of Equations
- 41: 21 In-Class Assignment - Solve Linear Systems of Equations using QR Decomposition
- 42: Supplemental Materials - Python Linear Algebra Packages
- 43: Jupyter Getting Started Guide
- 44: Python Linear Algebra Packages
- Back Matter
Thumbnail: A linear system in three variables determines a collection of planes The intersection point is the solution. (CC BY-SA 4.0; Fred the Oyster via Wikipedia).