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Applied Linear Algebra

  • Course level: All Levels

Description

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 11: Positive operators, isometries
Week 12:Polar and singular value decompositions

Linear Algebra INTENDED AUDIENCE: Senior level Undergraduate and First-year Postgraduate/PhD

Topics for this course

19 Lessons

Introduction to the Course

Vector Spaces: Introduction00:00:00
Linear Combinations and Span00:00:00
Subspaces, Linear Dependence and Independence00:00:00
Basis and Dimension00:00:00
Sums, Direct Sums and Gaussian Elimination00:00:00
Linear Maps and Matrices00:00:00
Null space, Range, Fundamental theorem of linear maps00:00:00
Column space, null space and rank of a matrix00:00:00
Algebraic operations on linear maps00:00:00
Invertible maps, Isomorphism, Operators00:00:00
Solving Linear Equations00:00:00
Invertible maps, Isomorphism, Operators00:00:00
Solving Linear Equations00:00:00
Elementary Row Operations00:00:00
Translates of a subspace, Quotient Spaces00:00:00
Row space and rank of a matrix00:00:00
Determinants00:00:00
Coordinates and linear maps under a change of basis00:00:00
Simplifying matrices of linear maps by choice of basis00:00:00
Free

Enrolment validity: Lifetime

Requirements

  • Basic Calculus, Should have done a basic (or a first) course in Linear Algebra