Linear algebra, seen before it is computed
Geometry first, then Strang's big picture, then the mechanics you can actually do by hand — and eigenvalues once they mean something.
67 sources·12 rooms
Published by learnthings · 2h ago
mathslinear algebra
You get your own copy — yours to change, and to take notes on.
Stage 1 · See it before you compute it
Essence of linear algebra (3Blue1Brown)
8- 1Vectors | Chapter 1, Essence of linear algebrayoutube.com
- 2Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebrayoutube.com
- 3Linear transformations and matrices | Chapter 3, Essence of linear algebrayoutube.com
- 4Matrix multiplication as composition | Chapter 4, Essence of linear algebrayoutube.com
- 5Three-dimensional linear transformations | Chapter 5, Essence of linear algebrayoutube.com
- 6The determinant | Chapter 6, Essence of linear algebrayoutube.com
- 7Inverse matrices, column space and null space | Chapter 7, Essence of linear algebrayoutube.com
- 8Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebrayoutube.com
The same intuition, in writing
3- 9An intuitive guide to linear algebrabetterexplained.com
- 10Immersive Linear Algebra — a book with live figuresimmersivemath.com
- 113Blue1Brown's own linear algebra page3blue1brown.com
Stage 2 · The whole picture
A vision of linear algebra (Gilbert Strang, MIT)
7- 12Intro: A New Way to Start Linear Algebrayoutube.com
- 13Part 1: The Column Space of a Matrixyoutube.com
- 14Part 2: The Big Picture of Linear Algebrayoutube.com
- 15Part 3: Orthogonal Vectorsyoutube.com
- 16Part 4: Eigenvalues and Eigenvectorsyoutube.com
- 17Part 5: Singular Values and Singular Vectorsyoutube.com
- 18Part 6: Finding the Nullspace: Solving Ax = 0 by Eliminationyoutube.com
The course and the book behind it
3- 19MIT 18.06 Linear Algebra — the full courseocw.mit.edu
- 20Strang's Introduction to Linear Algebramath.mit.edu
- 21Khan Academy's linear algebra track, for practice problemskhanacademy.org
Stage 3 · Work the mechanics
Full course: systems, elimination, spaces
16- 22What's the big idea of Linear Algebra? **Course Intro**youtube.com
- 23What is a Solution to a Linear System? **Intro**youtube.com
- 24Visualizing Solutions to Linear Systems - - 2D & 3D Cases Geometricallyyoutube.com
- 25Rewriting a Linear System using Matrix Notationyoutube.com
- 26Using Elementary Row Operations to Solve Systems of Linear Equationsyoutube.com
- 27Using Elementary Row Operations to simplify a linear systemyoutube.com
- 28Examples with 0, 1, and infinitely many solutions to linear systemsyoutube.com
- 29Row Echelon Form and Reduced Row Echelon Formyoutube.com
- 30Back Substitution with infinitely many solutionsyoutube.com
- 31The Gaussian Algorithm Visualizedyoutube.com
- 32What is a vector? Visualizing Vector Addition & Scalar Multiplicationyoutube.com
- 33Introducing Linear Combinations & Spanyoutube.com
- 34How to determine if one vector is in the span of other vectors?youtube.com
- 35Matrix-Vector Multiplication and the equation Ax=byoutube.com
- 36Matrix-Vector Multiplication Exampleyoutube.com
- 37Proving Algebraic Rules in Linear Algebra --- Ex: A(b+c) = Ab +Acyoutube.com
A textbook you can work straight through
2- 38Interactive Linear Algebra (Georgia Tech)textbooks.math.gatech.edu
- 39Introduction to Applied Linear Algebra — Boyd & Vandenberghe (free PDF)web.stanford.edu
Stage 4 · Determinants, eigenvalues, change of basis
The geometric versions
8- 40The determinant | Chapter 6, Essence of linear algebrayoutube.com
- 41Inverse matrices, column space and null space | Chapter 7, Essence of linear algebrayoutube.com
- 42Dot products and duality | Chapter 9, Essence of linear algebrayoutube.com
- 43Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebrayoutube.com
- 44Change of basis | Chapter 13, Essence of linear algebrayoutube.com
- 45Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebrayoutube.com
- 46A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebrayoutube.com
- 47Abstract vector spaces | Chapter 16, Essence of linear algebrayoutube.com
Factorisations, subspaces, least squares
3- 48Five Factorizations of a Matrixyoutube.com
- 49The Four Fundamental Subspaces and Least Squaresyoutube.com
- 50Elimination and Factorization A = CRyoutube.com
Later chapters of the full course
11- 51Visualizing Change Of Basis Dynamicallyyoutube.com
- 52Example: Writing a vector in a new basisyoutube.com
- 53What eigenvalues and eigenvectors mean geometricallyyoutube.com
- 54Using determinants to compute eigenvalues & eigenvectorsyoutube.com
- 55Example: Computing Eigenvalues and Eigenvectorsyoutube.com
- 56A range of possibilities for eigenvalues and eigenvectorsyoutube.com
- 57Diagonal Matrices are Freaking Awesomeyoutube.com
- 58How the Diagonalization Process Worksyoutube.com
- 59Compute large powers of a matrix via diagonalizationyoutube.com
- 60Full Example: Diagonalizing a Matrixyoutube.com
- 61COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**youtube.com
Stage 5 · Where this is going
Matrices as the language of data
2The courses these videos come from
3How to use this path
1- 67Watch first, then grind