Lecture Notes For Linear Algebra Gilbert Strang -

Gilbert Strang’s 18.06 Linear Algebra lectures at MIT are legendary because they shift the focus from tedious matrix calculations to the beautiful geometric intuition behind the math.

Option A: Cornell Method (Modified)

• Pass 1 (Watch at 1.25x speed): Do not write full sentences. Instead, draw the matrices. Strang is visual—copy his matrices exactly as he writes them. Use arrows to show how rows combine.
• Pass 2 (Immediately after the lecture): Rewrite your scrappy notes into a structured document. This is where you solve the “check yourself” problems he throws out mid-lecture.

• SVD (Lec 29): The ultimate connection: (A = U\Sigma V^T).
  In your notes, draw a mapping diagram:
  (V^T) (rotate in row space) → (\Sigma) (scale) → (U) (rotate into column space).
• Pseudoinverse (Lec 33): (A^+ = V\Sigma^+ U^T). Note: “Solves (Ax = b) when (A) isn’t square or invertible.”