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).