MLND MIT 18.06

This is the page for the MIT 18.06 Linear Algebra course hosted by the Machine Learning Nanodegree Slack group.

Click here to enroll and go here to view the list of enrolled students

Every "week" (the pacing may change) there will be new topics and homework that you can work through. The current week's content will be available on this GitHub page and past weeks are in the Wiki.

Discussion/Questions

If you want to discuss or ask any questions, you can either drop a message in the #mit_1806 channel in the MLND Slack Group, or open an GitHub "issue" at the top of the page (we treat these like forum threads). Please label your thread with the correct tags so that people can find what they are looking for.

Don't be shy to ask any questions, we don't bite and the chances are that someone else is wondering about the same thing! :)

Course Goals

To explore:

1. Linear combinations (alpha*u+beta*v+...) and their spans
2. The solutions to Ax=b and Ax=lambda*x
3. The practical applications of these

Notation:

• Greek letters are scalars i.e. lambda in \R
• Lower case letters are vectors
• Capital letters are matrices

Resources:

• YouTube Playlist
• Download All The Videos
• MIT OCW Course
• [Textbook] (http://facultymember.iaukhsh.ac.ir/images/Uploaded_files/[Strang_G.]_Linear_algebra_and_its_applications(4)[5881001].PDF)
• Another Student's work through the course

Homework

Homework is provided by @joshuacook. It is unique to this course! Two options to get it: fork this repo and do it locally. Please submit a pull request to upload your finished version when you are done. (Make sure to rename the file!) OR you can do it online with a shared jupyternotebook

Homework 1 (due 9/5/2016)

Learning goals:

• Get started with course
• Begin to think about row view versus column view
• Understand linear combinations
• Begin to think about numpy in the context of linear algebra

Watch Videos

• Lecture 1: The geometry of linear equations
• Lecture 2: Elimination with matrices.

Complete Homework 1

Homework 2 (due 9/14/2016)

• Lecture 3: Multiplication and inverse matrices
• Lecture 4: Factorization into A = LU

Complete Homework 2

Homework 3 (due 9/23/2016)

• Lecture 5: Transposes, permutations, spaces R^n
• Lecture 6: Column space and nullspace

Homework 4 (due 9/30/2016)

• Lecture 7: Solving Ax = 0: pivot variables, special solutions
• Lecture 8: Solving Ax = b: row reduced form R

Homework 5 (due 10/9/2016)

• Lecture 9: Independence, basis, and dimension
• Lecture 10: The four fundamental subspaces

Homework 6 (due 10/18/2016)

• Lecture 11: Matrix spaces; rank 1; small world graphs
• Lecture 12: Graphs, networks, incidence matrices

Lecture 13: Quiz 1 review

Take Home Quiz 1 due 10/30/16

Homework 6 (due 11/9/16)

• Lecture 14: Orthogonal vectors and subspaces
• Lecture 15: Projections onto subspaces

Homework 7 (due 11/18/16)

• Lecture 16: Projection matrices and least squares
• Lecture 17: Orthogonal matrices and Gram-Schmidt

Homework 8 (due 11/27/16)

• Lecture 18: Properties of determinants
• Lecture 19: Determinant formulas and cofactors
• Lecture 20: Cramer's rule, inverse matrix, and volume

Homework 9 (due 12/8/16)

• Lecture 21: Eigenvalues and eigenvectors
• Lecture 22: Diagonalization and powers of A

Homework 10 (due 12/17/16)

• Lecture 23: Differential equations and exp(At)
• Lecture 24: Markov matrices; fourier series

Take Home Quiz 2 due 1/3/17

Homework 11 (due 1/12/17)

• Lecture 25: Symmetric matrices and positive definiteness
• Lecture 26: Complex matrices; fast fourier transform

Homework 12 (due 1/21/17)

• Lecture 27: Positive definite matrices and minima
• Lecture 28: Similar matrices and jordan form

Homework 13 (due 1/30/17)

• Lecture 29: Singular value decomposition
• Lecture 30: Linear transformations and their matrices

Homework 14 (due 2/8/17)

• Lecture 31: Change of basis; image compression
• Lecture 33: Left and right inverses; pseudoinverse

Take Home Final Exam due 2/20/17