Advanced Linear Algebra
Unlock the Power of Vector Spaces: Master Advanced Linear Algebra with Professor Macauley. Dive deep into theory and applications, from eigenvectors to spectral theorems. Enhance your mathematical prowess and transform complex problems into elegant solutions.
5.0
(4)
43 learners
What you'll learn
- Understand key concepts of vector spaces, including spanning, independence, and bases.
- Analyze the role of eigenvalues, eigenvectors, and the spectral theorem in linear mappings.
- Apply the Gram-Schmidt process and orthogonal projection in various contexts.
- Evaluate the properties and applications of quadratic forms and spectral resolutions.
This course includes
- 25.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 42 lessons • 25.5 hours of video
Mastering Advanced Linear Algebra: Concepts and Applications
42 lessons
• 25.5 hours
Mastering Advanced Linear Algebra: Concepts and Applications
42 lessons
• 25.5 hours
- Advanced Linear Algebra, Lecture 1.1: Vector spaces and linearity 36:25
- Advanced Linear Algebra, Lecture 1.2: Spanning, independence, and bases 39:25
- Advanced Linear Algebra, Lecture 1.3: Direct sums and products 19:24
- Advanced Linear Algebra, Lecture 1.4: Quotient spaces 43:57
- Advanced Linear Algebra, Lecture 1.5: Dual vector spaces 23:36
- Advanced Linear Algebra, Lecture 1.6: Annihilators 29:07
- Advanced Linear Algebra, Lecture 2.1: Rank and nullity 31:31
- Advanced Linear Algebra, Lecture 2.2: Applications of the rank-nullity theorem 38:40
- Advanced Linear Algebra, Lecture 2.3: Algebra of linear mappings 35:24
- Advanced Linear Algebra, Lecture 2.4: The four subspaces 43:09
- Advanced Linear Algebra, Lecture 2.5: The transpose of a linear map 41:07
- Advanced Linear Algebra, Lecture 2.6: Matrices 41:51
- Advanced Linear Algebra, Lecture 2.7: Change of basis 21:08
- Advanced Linear Algebra, Lecture 3.1: Determinant prerequisites 27:11
- Advanced Linear Algebra, Lecture 3.2: Symmetric and skew-symmetric multilinear forms 30:52
- Advanced Linear Algebra, Lecture 3.3: Alternating multilinear forms 41:57
- Advanced Linear Algebra, Lecture 3.4: The determinant of a linear map 33:30
- Advanced Linear Algebra, Lecture 3.5: The determinant and trace of a matrix 33:38
- Advanced Linear Algebra, Lecture 3.6: Minors and cofactors 31:34
- Advanced Linear Algebra, Lecture 3.7: Tensors 56:25
- Advanced Linear Algebra, Lecture 4.1: Eigenvalues and eigenvectors 39:44
- Advanced Linear Algebra, Lecture 4.2: The Cayley-Hamilton theorem 49:20
- Advanced Linear Algebra, Lecture 4.3: Generalized eigenvectors 29:29
- Advanced Linear Algebra, Lecture 4.4: Invariant subspaces 41:31
- Advanced Linear Algebra, Lecture 4.5: The spectral theorem 32:59
- Advanced Linear Algebra, Lecture 4.6: Generalized eigenspaces 26:41
- Advanced Linear Algebra, Lecture 4.7: Jordan canonical form 31:50
- Advanced Linear Algebra, Lecture 5.1: Inner products and Euclidean structure 41:52
- Advanced Linear Algebra, Lecture 5.2: Orthogonality 48:14
- Advanced Linear Algebra, Lecture 5.3: Gram-Schmidt and orthogonal projection 52:30
- Advanced Linear Algebra, Lecture 5.4: Adjoints 20:18
- Advanced Linear Algebra, Lecture 5.5: Projection and Least Squares 36:31
- Advanced Linear Algebra, Lecture 5.6: Isometries 32:19
- Advanced Linear Algebra, Lecture 5.7: The norm of a linear map 47:07
- Advanced Linear Algebra, Lecture 5.9: Complex inner product spaces 29:54
- Advanced Linear Algebra, Lecture 6.1: Quadratic forms 36:12
- Advanced Linear Algebra, Lecture 6.2: Spectral resolutions 38:56
- Advanced Linear Algebra, Lecture 6.3: Normal linear maps 35:08
- Advanced Linear Algebra, Lecture 6.4: The Rayleigh quotient 53:09
- Advanced Linear Algebra Lecture 6.5: Self-adjoint differential operators 44:50
- Advanced Linear Algebra, Lecture 7.1: Definiteness and indefiniteness 34:42
- Advanced Linear Algebra, Lecture 7.2: Nonstandard inner products and Gram matrices 40:49
Related learning topics
Take this course with you
Download the app to continue lessons from your phone anytime.
