This glossary is cumulative. New entries are added each chapter, and every chapter links back here. Every symbol is explained on its first appearance in the course.
| Letter | Name | Pronounced | Used for |
|---|---|---|---|
| α, Α | alpha | al-fah | Learning rate, significance level, smoothing factor |
| β, Β | beta | bay-tah | Momentum coefficient, regularization strength, regression coefficient |
| γ, Γ | gamma | gam-ah | Learning rate schedule, discount factor in RL |
| δ, Δ | delta | del-tah | Small change (δ), large change (Δ), Kronecker delta |
| ε, Ε | epsilon | ep-sih-lon | Small constant (avoiding division by zero), exploration rate |
| ζ, Ζ | zeta | zay-tah | Riemann zeta function |
| η, Η | eta | ee-tah / ay-tah | Learning rate in gradient descent |
| θ, Θ | theta | thay-tah | Parameters / weights of a model |
| ι, Ι | iota | eye-oh-tah | Very small amount ("iota") |
| κ, Κ | kappa | kap-ah | Condition number, curvature |
| λ, Λ | lambda | lam-dah | Regularization coefficient, eigenvalues, Lagrangian multiplier |
| μ, Μ | mu | myoo | Mean of a distribution, learning rate scaling |
| ν, Ν | nu | nyoo | Degrees of freedom, learning rate schedule |
| ξ, Ξ | xi | ksee | Random noise variable, latent variable |
| ο, Ο | omicron | om-ih-cron | (rare in ML) |
| π, Π | pi | pie | 3.14159…, product notation (Π) |
| ρ, Ρ | rho | roe | Correlation coefficient, learning rate decay |
| σ, Σ | sigma | sig-mah | Standard deviation (σ), activation function (sigmoid), summation (Σ) |
| τ, Τ | tau | tah-oo / tow | Temperature parameter, time constant |
| υ, Υ | upsilon | up-sih-lon / yoop-sih-lon | (rare in ML) |
| φ, Φ | phi | fye / fee | Activation function, feature map, cumulative distribution function |
| χ, Χ | chi | kai (rhymes with "eye") | Chi-squared distribution |
| ψ, Ψ | psi | sigh / psigh | Wavefunction, state representation |
| ω, Ω | omega | oh-may-gah | Angular frequency, sample space |
| Symbol | Name | Meaning |
|---|---|---|
| ∇ | Nabla / del | Gradient operator — vector of partial derivatives |
| ∂ | Partial derivative | Derivative with respect to one variable while holding others constant |
| ∂f/∂x | Partial derivative of f w.r.t. x | Rate of change of f as x changes |
| df/dx | Total derivative | Derivative of f with respect to x (single variable) |
| ∑ | Summation | Sum over a range: ∑ᵢ₌₁ⁿ xᵢ = x₁ + x₂ + … + xₙ |
| ∏ | Product | Product over a range: ∏ᵢ₌₁ⁿ xᵢ = x₁ · x₂ · … · xₙ |
| ∫ | Integral | Continuous summation / area under curve |
| ∈ | Set membership | "is an element of": x ∈ ℝ means "x is a real number" |
| ∉ | Not in | "is not an element of" |
| ∀ | For all | Universal quantifier: ∀x means "for all x" |
| ∃ | There exists | Existential quantifier: ∃x means "there exists an x" |
| ∄ | There does not exist | Negation of ∃ |
| ⊂, ⊆ | Subset, subset or equal | A ⊆ B means "every element of A is also in B" |
| ∪ | Union | Set of elements in A or B (or both) |
| ∩ | Intersection | Set of elements in both A and B |
| ∅ | Empty set | Set with no elements |
| → | Maps to | Function: f: ℝ → ℝ means f takes a real number and returns one |
| ↦ | Maps to (element) | f: x ↦ x² means f applied to x gives x² |
| ⊗ | Tensor product | Outer product / Kronecker product |
| ⊕ | Direct sum | Concatenation / block-diagonal combination |
| ⊙ | Hadamard product | Element-wise multiplication |
| ⟨·,·⟩ | Inner product | Dot product: ⟨u, v⟩ = uᵀv |
| ∥·∥ | Norm | Length: ∥v∥₂ = √(v₁² + … + vₙ²) |
| ∥·∥ₚ | p-norm | ∥v∥ₚ = (∑ |
| ∝ | Proportional to | Equals up to a constant factor: f ∝ g means f = c·g |
| ∼ | Distributed as | x ∼ N(0,1) means x is normally distributed |
| ≈ | Approximately equal | Close but not exactly equal |
| ≡ | Identically equal | Equal by definition: f(x) ≡ g(x) for all x |
| ≪, ≫ | Much less/greater | Order of magnitude difference |
| ⊥ | Orthogonal / perpendicular | Perpendicular vectors, independent events |
| ∥ | Parallel | Parallel vectors |
| ∴ | Therefore | Logical conclusion |
| ∵ | Because | Justification |
| □ | QED | End of proof |
| ∞ | Infinity | Unbounded / arbitrarily large |
| | | | Absolute value | Distance from zero: |x| = x if x ≥ 0, -x if x < 0 |
| Symbol | Name | Meaning |
|---|---|---|
| ℝ | Real numbers | All numbers on the number line |
| ℕ | Natural numbers | 1, 2, 3, … (sometimes includes 0) |
| ℤ | Integers | …, -2, -1, 0, 1, 2, … |
| ℚ | Rational numbers | Numbers expressible as p/q |
| ℂ | Complex numbers | Numbers of the form a + bi |
| ℝⁿ | n-dimensional real space | Vectors of n real numbers |
| ℝ^{m×n} | m×n real matrices | Matrices with m rows and n columns |
| 𝕊ⁿ | Symmetric n×n matrices | Matrices where A = Aᵀ |
| Notation | Name | Meaning |
|---|---|---|
| e | Euler's number | ~2.71828, base of natural logarithms |
| i | Imaginary unit | i = √(−1) |
| π | Pi | ~3.14159, ratio of circumference to diameter |
| τ | Tau | 2π = ~6.28318 |
| ε₀ | Epsilon naught | Positive small number used in proofs |
| δᵢⱼ | Kronecker delta | 1 if i = j, 0 otherwise |
| sgn(x) | Sign function | 1 if x > 0, -1 if x < 0, 0 if x = 0 |
| ⌊x⌋ | Floor | Largest integer ≤ x |
| ⌈x⌉ | Ceiling | Smallest integer ≥ x |
| [x] | Nearest integer | Round to closest integer |
| {x} | Fractional part | x — ⌊x⌋ |
| mod | Modulo | Remainder after division |
| |S| | Cardinality | Number of elements in set S |
| 𝒪(·) | Big-O | Asymptotic upper bound |
| Θ(·) | Big-Theta | Asymptotically tight bound |
| Ω(·) | Big-Omega | Asymptotic lower bound |
| o(·) | Little-o | Strictly smaller asymptotically |
| Notation | Name | Meaning |
|---|---|---|
| $\hat{\mathbf{v}}$ | Hat / unit vector | A vector of length 1: $\hat{\mathbf{v}} = \mathbf{v} / |\mathbf{v}|$ |
| $\perp$ | Orthogonal / perpendicular | $\mathbf{u} \perp \mathbf{v}$ means $\langle \mathbf{u}, \mathbf{v} \rangle = 0$ |
| Notation | Name | Meaning |
|---|---|---|
| $\mathbb{R}^{m \times n}$ | Matrix space | The set of all $m \times n$ real matrices |
| $\mathbf{A}_{ij}$ or $a_{ij}$ | Matrix element | The entry in row $i$, column $j$ of $\mathbf{A}$ |
| $\mathbf{A}^T$ | Transpose | $\mathbf{A}$ with rows and columns swapped: $(\mathbf{A}^T)_{ij} = \mathbf{A}_{ji}$ |
| $\mathbf{I}_n$ | Identity matrix | $n \times n$ matrix with 1s on the diagonal, 0s elsewhere |
| $\delta_{ij}$ | Kronecker delta | $1$ if $i = j$, $0$ otherwise |
| Notation | Name | Meaning |
|---|---|---|
| $\mathbf{A}^{-1}$ | Matrix inverse | The unique matrix satisfying $\mathbf{A}\mathbf{A}^{-1} = \mathbf{A}^{-1}\mathbf{A} = \mathbf{I}_n$; "undoes" the transformation $\mathbf{A}$ |
| $[\mathbf{A} \mid \mathbf{I}]$ | Augmented matrix | $\mathbf{A}$ with the identity stacked to its right; Gauss-Jordan reduces this to $[\mathbf{I} \mid \mathbf{A}^{-1}]$ |
| $\nexists\,\mathbf{A}^{-1}$ | Singular / non-invertible | A square matrix with no inverse — it collapses some direction to zero |
| $ad - bc$ | 2×2 determinant (preview) | Denominator of the 2×2 inverse formula; zero $\Rightarrow$ singular. Formalized in ch07 |
| Notation | Name | Meaning |
|---|---|---|
| $\det(\mathbf{A})$ or $|\mathbf{A}|$ | Determinant | The signed area/volume scaling factor of the transformation $\mathbf{A}$; zero $\Leftrightarrow$ $\mathbf{A}$ is singular |
| $M_{ij}$ | Minor | The $(n-1)\times(n-1)$ matrix obtained by deleting row $i$ and column $j$ of $\mathbf{A}$ |
| $C_{ij}$ | Cofactor | The signed minor: $C_{ij} = (-1)^{i+j}\det(M_{ij})$ |
| $(-1)^{i+j}$ | Checkerboard sign | Alternating $+/-$ pattern (top-left $+$) used by cofactor expansion |
This glossary is a living document. Each chapter adds new entries as symbols are introduced.