σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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Skills›Linear Algebra
L

Linear Algebra Skill

LiveStart here

Almost every quant model is a matrix problem in disguise: a portfolio is a vector, a covariance is a matrix, a regression is a projection. This skill builds the ideas with short checks (matrices you fill in, numbers you compute, expressions you type) and finance examples, then turns them into algorithms: LU, QR and Cholesky. It ends with a code lab that fits a regression on real stock returns using only your own solver and checks it against NumPy.

4 modules12 graded labs~10 hoursBeginner → Intermediate
Start skill

Syllabus

12 topics · open any topic, in any order
  1. 1Vectors and dot productsNot startedRequires Python40 minStart
  2. 2Matrices as linear mapsNot started40 minStart
  3. 3Matrix multiplication and its costNot started40 minStart
  1. 4Matrices and linear systemsNot startedRequires Python45 minStart
  2. 5LU decompositionNot started50 minStart
  3. 6Inverse and conditioningNot started50 minStart
  1. 7Rank and null spaceNot started50 minStart
  2. 8Orthogonality and projectionsNot started45 minStart
  1. 9Least squares and the normal equationsNot started55 minStart
  2. 10QR decomposition and Gram-SchmidtNot started50 minStart
  3. 11Cholesky and positive-definite matricesNot started50 minStart
  4. 12Capstone: OLS regression from scratchNot started1 hr 30 minStart

What you'll learn

  • Read a matrix as a linear map and multiply matrices, knowing what the product costs
  • Solve systems with Gaussian elimination and LU, and judge a solution by the determinant and the condition number
  • Find rank, null space and orthogonal projections, and know when a system has no, one or many solutions
  • Fit least squares through the normal equations, QR and Cholesky, and know why QR is the safer route
  • Build an OLS regression of a stock on the market with your own solver and check it against NumPy

Tools you'll use

PythonNumPypytest

Completion

Pass all 12 labs with a score of 70+ to complete the skill and earn the Linear Algebra for Quants badge on your profile.

0 / 120%

Prerequisites

High-school maths is enough. The two Python topics inside this skill help, but you can start without them.

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