Learn Linear Algebra in this 20-hour college course. Watch the second half here: https://youtu.be/DJ6YwBN7Ya8
This course is taught by Dr. Jim Hefferon, a professor of mathematics at St Michael’s College.
? The course follows along with Dr. Hefferon’s Linear Algebra text book. The book is available for free: http://joshua.smcvt.edu/linearalgebra/book.pdf
? Access additional course resources at: https://hefferon.net/linearalgebra/
? Stephen Chew’s Learning How to Learn series: https://www.youtube.com/watch?v=htv6eap1-_M&list=PL85708E6EA236E3DB
? 3Blue1Brown’s Linear Algebra series: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
?? Course Contents ??
?? (0:00:00) Introduction to Linear Algebra by Hefferon
?? (0:04:35) One.I.1 Solving Linear Systems, Part One
?? (0:26:08) One.I.1 Solving Linear Systems, Part Two
?? (0:40:56) One.I.2 Describing Solution Sets, Part One
?? (0:54:21) One.I.2 Describing Solution Sets, Part Two
?? (1:02:48) One.I.3 General = Particular + Homogeneous
?? (1:18:33) One.II.1 Vectors in Space
?? (1:35:08) One.II.2 Vector Length and Angle Measure
?? (1:51:31) One.III.1 Gauss-Jordan Elimination
?? (2:00:00) One.III.2 The Linear Combination Lemma
?? (2:44:32) Two.I.1 Vector Spaces, Part One
?? (3:08:12) Two.I.1 Vector Spaces, Part Two
?? (3:33:01) Two.I.2 Subspaces, Part One
?? (3:58:16) Two.I.2 Subspaces, Part Two
?? (4:23:43) Two.II.1 Linear Independence, Part One
?? (4:45:11) Two.II.1 Linear Independence, Part Two
?? (5:03:57) Two.III.1 Basis, Part One
?? (5:23:55) Two.III.1 Basis, Part Two
?? (5:42:34) Two.III.2 Dimension
?? (6:03:24) Two.III.3 Vector Spaces and Linear Systems
?? (6:25:09) Three.I.1 Isomorphism, Part One
?? (6:54:08) Three.I.1 Isomorphism, Part Two
?? (7:21:47) Three.I.2 Dimension Characterizes Isomorphism
?? (7:43:43) Three.II.1 Homomorphism, Part One
?? (8:14:52) Three.II.1 Homomorphism, Part Two
?? (8:30:24) Three.II.2 Range Space and Null Space, Part One
?? (9:00:17) Three.II.2 Range Space and Null Space, Part Two.
?? (9:20:57) Three.II Extra Transformations of the Plane
?? (9:52:06) Three.III.1 Representing Linear Maps, Part One.
?? (10:13:18) Three.III.1 Representing Linear Maps, Part Two
?? (10:34:18) Three.III.2 Any Matrix Represents a Linear Map
?? (10:58:32) Three.IV.1 Sums and Scalar Products of Matrices
?? (11:19:14) Three.IV.2 Matrix Multiplication, Part One
?? (11:39:44) Three.IV.2 Matrix Multiplication, Part Two
The following sections are in the second video: https://youtu.be/DJ6YwBN7Ya8
?? Three.IV.3 Mechanics of Matrix Multiplication
?? Three.IV.4 Matrix Inverse, Part One
?? Three.IV.4 Matrix Inverse, Part Two
?? Three.V.1 Changing Vector Representations
?? Three.V.2 Changing Map Representations, Part One
?? Three.V.2 Changing Map Representations, Part Two
?? Three.VI Projection
?? Four.I.1 Determinants
?? Four.I.3 Permutation Expansion, Part One
?? Four.I.3 Permutation Expansion, Part Two
?? Four.I.4 Determinants Exist (optional)
?? Four.II.1 Geometry of Determinants
?? Four.III.1 Laplace’s formula for the determinant
?? Five.I.1 Complex Vector Spaces
?? Five.II.1 Similarity
?? Five.II.2 Diagonalizability
?? Five.II.3 Eigenvalues and Eigenvectors, Part One
?? Five.II.3 Eigenvalues and Eigenvectors, Part Two
?? Five.II.3 Geometry of Eigenvalues and Eigenvectors
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