Mastering Advanced Linear Algebra: Concepts and Applications
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.
4.0(10)
139 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
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Advanced Linear Algebra, Lecture 1.1: Vector spaces and linearity36:24
Advanced Linear Algebra, Lecture 1.2: Spanning, independence, and bases39:24
Advanced Linear Algebra, Lecture 1.3: Direct sums and products19:24
Advanced Linear Algebra, Lecture 1.4: Quotient spaces43:56
Advanced Linear Algebra, Lecture 1.5: Dual vector spaces23:35
Advanced Linear Algebra, Lecture 1.6: Annihilators29:06
Advanced Linear Algebra, Lecture 2.1: Rank and nullity31:31
Advanced Linear Algebra, Lecture 2.2: Applications of the rank-nullity theorem38:39
Advanced Linear Algebra, Lecture 2.3: Algebra of linear mappings35:23
Advanced Linear Algebra, Lecture 2.4: The four subspaces43:08
Advanced Linear Algebra, Lecture 2.5: The transpose of a linear map41:06
Advanced Linear Algebra, Lecture 2.6: Matrices41:50
Advanced Linear Algebra, Lecture 2.7: Change of basis21:07
Advanced Linear Algebra, Lecture 3.1: Determinant prerequisites27:11
Advanced Linear Algebra, Lecture 3.2: Symmetric and skew-symmetric multilinear forms30:51
Advanced Linear Algebra, Lecture 3.3: Alternating multilinear forms41:57
Advanced Linear Algebra, Lecture 3.4: The determinant of a linear map33:29
Advanced Linear Algebra, Lecture 3.5: The determinant and trace of a matrix33:38
Advanced Linear Algebra, Lecture 3.6: Minors and cofactors31:33
Advanced Linear Algebra, Lecture 3.7: Tensors56:24
Advanced Linear Algebra, Lecture 4.1: Eigenvalues and eigenvectors39:44
Advanced Linear Algebra, Lecture 4.2: The Cayley-Hamilton theorem49:20
Advanced Linear Algebra, Lecture 4.3: Generalized eigenvectors29:28
Advanced Linear Algebra, Lecture 4.4: Invariant subspaces41:31
Advanced Linear Algebra, Lecture 4.5: The spectral theorem32:59
Advanced Linear Algebra, Lecture 4.6: Generalized eigenspaces26:41
Advanced Linear Algebra, Lecture 4.7: Jordan canonical form31:50
Advanced Linear Algebra, Lecture 5.1: Inner products and Euclidean structure41:51
Advanced Linear Algebra, Lecture 5.2: Orthogonality48:13
Advanced Linear Algebra, Lecture 5.3: Gram-Schmidt and orthogonal projection52:30
Advanced Linear Algebra, Lecture 5.4: Adjoints20:18
Advanced Linear Algebra, Lecture 5.5: Projection and Least Squares36:31
Advanced Linear Algebra, Lecture 5.6: Isometries32:19
Advanced Linear Algebra, Lecture 5.7: The norm of a linear map47:06
Advanced Linear Algebra, Lecture 5.9: Complex inner product spaces29:54
Advanced Linear Algebra, Lecture 6.1: Quadratic forms36:11
Advanced Linear Algebra, Lecture 6.2: Spectral resolutions38:56
Advanced Linear Algebra, Lecture 6.3: Normal linear maps35:07
Advanced Linear Algebra, Lecture 6.4: The Rayleigh quotient53:08
Advanced Linear Algebra Lecture 6.5: Self-adjoint differential operators44:50
Advanced Linear Algebra, Lecture 7.1: Definiteness and indefiniteness34:42
Advanced Linear Algebra, Lecture 7.2: Nonstandard inner products and Gram matrices40:49
