| a, b, c, α, β, γ |
Scalars (lowercase) |
|
| x, y, z |
Vectors (bold lowercase) |
Section 1.1, 2.0 |
| A, B, C |
Matrices (bold uppercase) |
Section 2.1, 2.2 |
| \(x^\top, A^\top\) |
Transpose of a vector or matrix |
Section 2.2 |
| \(A^{-1}\) |
Inverse of a matrix |
Section 2.2 |
| \(\langle x, y \rangle\) |
Inner product of \(x\) and \(y\) |
Section 4.2 |
| \(x^\top y\) |
Dot product of \(x\) and \(y\) |
Section 2.0, 4.2 |
| \(B = (b_1, b_2, b_3)\) |
Ordered tuple |
|
| \(B = [b_1, b_2, b_3]\) |
Matrix of column vectors stacked horizontally |
Section 2.6 |
| \(B = \{b_1, b_2, b_3\}\) |
Set of vectors (unordered) |
Section 2.6 |
| \(\mathbb{Z}, \mathbb{N}\) |
Integers and natural numbers |
|
| \(\mathbb{R}, \mathbb{C}\) |
Real and complex numbers |
|
| \(\mathbb{R}^n\) |
\(n\)-dimensional vector space of reals |
|
| \(\forall x\) |
Universal quantifier (“for all \(x\)”) |
|
| \(\exists x\) |
Existential quantifier (“there exists \(x\)”) |
|
| \(a := b\) |
\(a\) is defined as \(b\) |
|
| \(a =: b\) |
\(b\) is defined as \(a\) |
|
| \(a \propto b\) |
\(a\) is proportional to \(b\) (\(a = \text{constant} \cdot b\)) |
|
| \(g \circ f\) |
Function composition (“\(g\) after \(f\)”) |
|
| \(\Leftrightarrow\) |
If and only if |
|
| \(\Rightarrow\) |
Implies |
|
| \(A, C\) |
Sets |
|
| \(a \in A\) |
\(a\) is an element of \(A\) |
|
| \(\emptyset\) |
Empty set |
|
| \(A \setminus B\) |
Elements in \(A\) but not in \(B\) |
Section 2.3 |
| \(D\) |
Number of dimensions (\(d = 1, \dots, D\)) |
|
| \(N\) |
Number of data points (\(n = 1, \dots, N\)) |
|
| \(I_m\) |
Identity matrix of size \(m \times m\) |
Section 2.2 |
| \(0_{m,n}\) |
Matrix of zeros of size \(m \times n\) |
|
| \(1_{m,n}\) |
Matrix of ones of size \(m \times n\) |
|
| \(e_i\) |
Standard (canonical) basis vector (1 in the \(i\)-th position) |
Section 2.6 |
dim |
Dimensionality of a vector space |
Section 2.6 |
rk(A) |
Rank of matrix \(A\) |
Section 2.6 |
Im(Φ) |
Image of a linear mapping \(Φ\) |
Section 2.7 |
ker(Φ) |
Kernel (null space) of \(Φ\) |
Section 2.6 |
span[b₁] |
Span (generating set) of \(b_1\) |
Section 2.6 |
tr(A) |
Trace of \(A\) |
Section 4.1 |
det(A) |
Determinant of \(A\) |
Section 2.2, 4.1 |
| \(| \cdot |\) |
Absolute value or determinant (depending on context) |
|
| \(\| \cdot \|\) |
Norm (Euclidean unless stated otherwise) |
Section 3.1 |
| \(\lambda\) |
Eigenvalue or Lagrange multiplier |
|
| \(E_\lambda\) |
Eigenspace corresponding to eigenvalue \(\lambda\) |
|
| \(x \perp y\) |
\(x\) and \(y\) are orthogonal |
Section 3.2 |
| \(V\) |
Vector space |
Section 2.0, 2.4 |
| \(V^\perp\) |
Orthogonal complement of \(V\) |
Section 3.6 |
| \(\sum_{n=1}^N x_n\) |
Sum: \(x_1 + \dots + x_N\) |
|
| \(\prod_{n=1}^N x_n\) |
Product: \(x_1 \cdot \dots \cdot x_N\) |
|
| \(\theta\) |
Parameter vector |
|
| \(\frac{\partial f}{\partial x}\) |
Partial derivative of \(f\) with respect to \(x\) |
|
| \(\frac{df}{dx}\) |
Total derivative of \(f\) with respect to \(x\) |
|
| \(\nabla\) |
Gradient |
|
| \(f^* = \min_x f(x)\) |
Minimum value of \(f\) |
|
| \(x^* \in \arg\min_x f(x)\) |
Value \(x^*\) that minimizes \(f\) |
|
| \(\mathcal{L}\) |
Lagrangian |
|
| \(\mathcal{L}\) |
Negative log-likelihood |
|
| \(\binom{n}{k}\) |
Binomial coefficient, \(n\) choose \(k\) |
|
| \(V_X[x]\) |
Variance of \(x\) with respect to the random variable \(X\) |
|
| \(E_X[x]\) |
Expectation of \(x\) with respect to the random variable \(X\) |
|
| \(\mathrm{Cov}_{X,Y}[x, y]\) |
Covariance between \(x\) and \(y\) |
|
| \(X \perp\!\!\!\perp Y \mid Z\) |
\(X\) is conditionally independent of \(Y\) given \(Z\) |
|
| \(X \sim p\) |
Random variable \(X\) is distributed according to \(p\) |
|
| \(\mathcal{N}(\mu, \Sigma)\) |
Gaussian distribution with mean \(\mu\) and covariance \(\Sigma\) |
|
| \(\mathrm{Ber}(\mu)\) |
Bernoulli distribution with parameter \(\mu\) |
|
| \(\mathrm{Bin}(N, \mu)\) |
Binomial distribution with parameters \(N, \mu\) |
|
| \(\mathrm{Beta}(\alpha, \beta)\) |
Beta distribution with parameters \(\alpha, \beta\) |
|