Playlist Duration

Playlist · Dr. Trefor Bazett

Linear Algebra (Full Course)

by Dr. Trefor Bazett · 84 videos

Listed in Best free college math courses on YouTube, ranked by total hours

Total watch time

10h 50m

at 1× speed · exactly 10 hours, 50 minutes, 25 seconds at 1×

At an hour a day you'd finish in 11 days

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84 videos in blocks of 10 · each column is a block's total, to scale

1h 25m
1h 14m
1h 12m
1h 20m
1h 16m
55m 31s
1h 22m
1h 24m
40m 46s

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Videos (84)

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Videos to
Watched
1 What's the big idea of Linear Algebra? **Course Intro** 12:58 2018-02-18
2 What is a Solution to a Linear System? **Intro** 5:28 2018-04-28
3 Visualizing Solutions to Linear Systems - - 2D & 3D Cases Geometrically 8:19 2018-04-28
4 Rewriting a Linear System using Matrix Notation 3:10 2017-05-09
5 Using Elementary Row Operations to Solve Systems of Linear Equations 7:27 2017-05-09
6 Using Elementary Row Operations to simplify a linear system 9:35 2017-05-09
7 Examples with 0, 1, and infinitely many solutions to linear systems 6:30 2017-05-11
8 Row Echelon Form and Reduced Row Echelon Form 6:41 2017-05-11
9 Back Substitution with infinitely many solutions 11:05 2017-05-11
10 The Gaussian Algorithm Visualized 13:37 2024-10-01
11 What is a vector? Visualizing Vector Addition & Scalar Multiplication 6:40 2018-05-16
12 Introducing Linear Combinations & Span 9:34 2018-05-16
13 How to determine if one vector is in the span of other vectors? 5:00 2017-05-14
14 Matrix-Vector Multiplication and the equation Ax=b 6:59 2017-05-15
15 Matrix-Vector Multiplication Example 4:33 2017-05-15
16 Proving Algebraic Rules in Linear Algebra --- Ex: A(b+c) = Ab +Ac 8:25 2018-05-24
17 The Big Theorem, Part I 14:01 2017-05-15
18 Writing solutions to Ax=b in vector form 4:48 2017-05-20
19 Geometric View on Solutions to Ax=b and Ax=0. 6:21 2017-05-20
20 Three nice properties of homogeneous systems of linear equations 7:53 2017-05-21
21 Linear Dependence and Independence - Geometrically 8:16 2017-05-21
22 Determining Linear Independence vs Linear Dependence 6:39 2017-05-21
23 Making a Math Concept Map | Ex: Linear Independence 7:10 2018-06-19
24 Transformations and Matrix Transformations 5:16 2017-05-22
25 Three examples of Matrix Transformations 8:25 2017-05-22
26 Linear Transformations 8:28 2017-05-22
27 Are Matrix Transformations and Linear Transformation the same? Part I 3:04 2017-05-22
28 Every vector is a linear combination of the same n simple vectors! 6:37 2017-05-27
29 Matrix Transformations are the same thing as Linear Transformations 8:49 2017-05-27
30 Finding the Matrix of a Linear Transformation 9:18 2017-05-28
31 One-to-one, Onto, and the Big Theorem Part II 9:30 2017-05-28
32 The motivation and definition of Matrix Multiplication 10:12 2017-05-28
33 Computing matrix multiplication 5:37 2017-05-28
34 Visualizing Composition of Linear Transformations **aka Matrix Multiplication** 14:00 2018-06-04
35 Elementary Matrices 7:20 2017-06-05
36 You can "invert" matrices to solve equations...sometimes! 7:12 2017-06-05
37 Finding inverses to 2x2 matrices is easy! 3:04 2017-06-05
38 Find the Inverse of a Matrix 6:30 2017-06-06
39 When does a matrix fail to be invertible? Also more "Big Theorem". 8:45 2017-06-07
40 Visualizing Invertible Transformations (plus why we need one-to-one) 8:12 2018-06-10
41 Invertible Matrices correspond with Invertible Transformations **proof** 6:38 2018-06-10
42 Determinants - a "quick" computation to tell if a matrix is invertible 9:14 2017-06-10
43 Determinants can be computed along any row or column - choose the easiest! 3:43 2017-06-11
44 Vector Spaces | Definition & Examples 8:11 2018-06-16
45 The Vector Space of Polynomials: Span, Linear Independence, and Basis 12:50 2020-07-12
46 Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples 6:26 2018-06-16
47 The Span is a Subspace | Proof + Visualization 5:03 2018-06-16
48 The Null Space & Column Space of a Matrix | Algebraically & Geometrically 10:41 2018-06-16
49 The Basis of a Subspace 3:53 2017-06-18
50 Finding a Basis for the Nullspace or Column space of a matrix A 9:45 2017-06-18
51 Finding a basis for Col(A) when A is not in REF form. 2:37 2017-06-24
52 Coordinate Systems From Non-Standard Bases | Definitions + Visualization 6:34 2018-06-23
53 Writing Vectors in a New Coordinate System **Example** 3:52 2018-06-23
54 What Exactly are Grid Lines in Coordinate Systems? 5:16 2018-06-21
55 The Dimension of a Subspace | Definition + First Examples 5:11 2018-06-22
56 Computing Dimension of Null Space & Column Space 3:27 2018-06-23
57 The Dimension Theorem | Dim(Null(A)) + Dim(Col(A)) = n | Also, Rank! 4:02 2018-06-24
58 Changing Between Two Bases | Derivation + Example 7:55 2018-07-03
59 Visualizing Change Of Basis Dynamically 7:42 2018-07-04
60 Example: Writing a vector in a new basis 8:55 2017-06-24
61 What eigenvalues and eigenvectors mean geometrically 9:09 2017-06-27
62 Using determinants to compute eigenvalues & eigenvectors 4:36 2017-06-27
63 Example: Computing Eigenvalues and Eigenvectors 7:33 2017-06-27
64 A range of possibilities for eigenvalues and eigenvectors 9:47 2017-06-30
65 Diagonal Matrices are Freaking Awesome 6:28 2017-07-08
66 How the Diagonalization Process Works 7:30 2017-07-08
67 Compute large powers of a matrix via diagonalization 3:01 2017-07-09
68 Full Example: Diagonalizing a Matrix 10:08 2017-07-09
69 COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example** 14:10 2020-02-18
70 Visualizing Diagonalization & Eigenbases 9:46 2018-07-09
71 Similar matrices have similar properties 8:47 2017-07-03
72 The Similarity Relationship Represents a Change of Basis 9:59 2017-07-09
73 Dot Products and Length 7:23 2017-07-10
74 Distance, Angles, Orthogonality and Pythagoras for vectors 8:14 2017-07-10
75 Orthogonal bases are easy to work with! 4:50 2017-07-15
76 Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Complement 3:57 2017-07-15
77 The geometric view on orthogonal projections 11:07 2017-07-15
78 Orthogonal Decomposition Theorem Part II 11:25 2017-07-15
79 Proving that orthogonal projections are a form of minimization 7:05 2017-07-15
80 Using Gram-Schmidt to orthogonalize a basis 11:21 2017-07-22
81 Full example: using Gram-Schmidt 6:18 2017-07-22
82 Rotation Matrices || Linear Algebra Fundamentals 21:24 2025-11-17
83 Least Squares Approximations 7:28 2017-07-22
84 Reducing the Least Squares Approximation to solving a system 5:36 2017-07-22
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