About Course
Applied Linear Algebra
Introduce the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students.
Week 1: Vectors and vector spaces
Week 2:Linear maps I: Definition, Spaces associated with a map, Matrices
Week 3: Linear maps II: Invertible linear maps, Elementary row/column operations, Solving linear equations, Quotient space
Week 4: Linear maps III: Four fundamental spaces, Rank of a matrix, Determinants, Change of basis
Week 5:Eigenvalues and eigenvectors of linear operators
Week 6: Applications of eigenvalues
Week 7: Inner product spaces
Week 8:Projection and least squares
Week 9:Adjoint of linear maps and operators
Week 10:Self-adjoint and normal operators
Week 10:Self-adjoint and normal operators
Week 11: Positive operators, isometries
Week 12:Polar and singular value decompositions
Linear Algebra INTENDED AUDIENCE: Senior level Undergraduate and First-year Postgraduate/PhD
Course Content
Introduction to the Course
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Vector Spaces: Introduction
00:00 -
Linear Combinations and Span
00:00 -
Subspaces, Linear Dependence and Independence
00:00 -
Basis and Dimension
00:00 -
Sums, Direct Sums and Gaussian Elimination
00:00 -
Linear Maps and Matrices
00:00 -
Null space, Range, Fundamental theorem of linear maps
00:00 -
Column space, null space and rank of a matrix
00:00 -
Algebraic operations on linear maps
00:00 -
Invertible maps, Isomorphism, Operators
00:00 -
Solving Linear Equations
00:00 -
Invertible maps, Isomorphism, Operators
00:00 -
Solving Linear Equations
00:00 -
Elementary Row Operations
00:00 -
Translates of a subspace, Quotient Spaces
00:00 -
Row space and rank of a matrix
00:00 -
Determinants
00:00 -
Coordinates and linear maps under a change of basis
00:00 -
Simplifying matrices of linear maps by choice of basis
00:00
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