Applied Linear Algebra

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

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

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Course Content

Introduction to the Course

  • 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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