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Term 12 · Year 3

Term 12 — Advanced Linear Algebra and Synthesis

Vector spaces, eigenvalues, PCA, final integration of the program.

10 lessons  ·  10 published ·  ~32h of study

(Year 3 — Integral, ODEs, Inference, Linear Algebra)

Classes (didactic grouping)

Each Class groups 2–5 Lessons by topic. Click on a Lesson to study the content.

Class A — Vector spaces and transformations

~9h · 3 lessons
  1. Lesson 111
    Vector spaces: axioms, subspaces, basis, dimension
    Vectors as elements of a vector space, axioms
    published →
  2. Lesson 112
    Linear transformations
    T: V → W, matrix representation
    published →
  3. Lesson 113
    Kernel and Image
    ker(T), im(T), rank-nullity theorem
    published →

Class B — Eigenvalues, diagonalization, symmetric/orthogonal matrices

~9h · 3 lessons
  1. Lesson 114
    Eigenvalues and eigenvectors
    det(A - λI) = 0, geometric interpretation
    published →
  2. Lesson 115
    Diagonalization
    A = PDP⁻¹, when diagonalizable, applications
    published →
  3. Lesson 116
    Special matrices: symmetric, orthogonal, and Hermitian
    Symmetric, orthogonal, projection matrices
    published →

Class C — SVD and PCA

~6h · 2 lessons
  1. Lesson 117
    Singular Value Decomposition (SVD)
    A = UΣVᵀ, applications, intuition
    published →
  2. Lesson 118
    Principal Component Analysis (PCA)
    Eigendecomposition of covariance, dimensionality reduction
    published →

Class D — Synthesis (Black-Scholes) + Final workshop

~6h · 2 lessons
  1. Lesson 119
    Synthesis: Black-Scholes revisited
    Heat equation, change of variables, normal distribution
    published →
  2. Lesson 120
    Final Workshop
    40 problems from Years 1–3
    published →

Test yourself this term

There are 10 exam versions covering this term, each with answer key + step-by-step solutions. Take one after each group of lessons.

Open exams for Term 12 →