Lectures

You can download the lectures here. We will try to upload the annotated slides when needed.

• (MT-00) Introduction and logistics
  tl;dr: Logistics of this course (Description, Objectives, Contents, Evaluation, TAs, etc)
  [slides]
  

  Suggested Readings:

  • Geometry of Linear Equations: Sections 1.1 and 1.2 from Gilbert Strang 4E
• (MT-01) System of Linear Equations (Row and Column Pictures)
  tl;dr: Two different ways to interpret the same system of linear equations: Row and Column perspectives
  [slides] [annotated_slides]
  

  Suggested Readings:

  • Geometry of Linear Equations: Sections 1.2 and Problem set 1.2 from Gilbert Strang 4E
• (MT-02) Gaussian Elimination
  tl;dr: Intuitive approach to solve a system of linear equations.
  [slides] [Annotated-slides]
  

  Suggested Readings:

  • Gaussian Elimination: Sections 1.3 and 1.4 from Gilbert Strang 4E
• (MT-03) Triangular Factorization
  tl;dr: Factoring the coefficient matrix into a lower and an upper triangular matrix.
  [slides] [Annotated-slides]
  

  Suggested Readings:

  • Gaussian Elimination: Sections 1.4 and 1.5 from Gilbert Strang 4E
• (MT-04) Inverse of a Matrix
  tl;dr: Matrix that undoes a matrix.
  [Notes]
  

  Suggested Readings:

  • Gaussian Elimination: Sections 1.6 from Gilbert Strang 4E
• (MT-03) Transpose of a Matrix
  tl;dr: Turning rows of a matrix into columns.
  [Notes]
  

  Suggested Readings:

  • Gaussian Elimination: Sections 1.6 from Gilbert Strang 4E
• (MT-06) Vector Spaces and Subspaces
  tl;dr: Worlds in which the linear combinations live.
  [Slides]
  

  Suggested Readings:

  • Gaussian Elimination: Sections 2.1 from Gilbert Strang 4E
• (MT-07) Column Space and Null Space
  tl;dr: Possible outputs of A and inputs that kill A.
  [Slides] [Annotated-slides]
  

  Suggested Readings:

  • Gaussian Elimination: Sections 2.1 from Gilbert Strang 4E
• (MT-08) Complete solution to Ax=b
  tl;dr: Every solution to Ax=b.
  
  

  Suggested Readings:

  • Gaussian Elimination: Sections 2.2 from Gilbert Strang 4E