Common Symbol Table
Li
Li Wei
Common Symbol Table
Common Mathematical Symbols
| Symbol | Chinese Pronunciation | English Pronunciation | Meaning |
|---|---|---|---|
\lim |
极限 | /ˈlɪmɪt/ (Limit) | Limit symbol, e.g., \lim indicates the limit as a variable approaches a value. |
\varlimsup / \varliminf (or \limsup / \liminf) |
上极限 / 下极限 | /ˌlɪmˈsʌp/ / /ˌlɪmˈɪnf/ (Limit superior / inferior) | Upper and lower limits of a sequence, e.g., \varlimsup or \varliminf. |
| 小 o | Little‑o notation | — | Higher‑order infinitesimal; o(f) means the term is of smaller order than f. |
| 大 O | Big‑O notation | — | Same or lower order infinitesimal; O(f) means the term is bounded by a constant times f. |
| 等价 / 相似 | Equivalent to / Similar to | — | Equivalent infinitesimals (e.g., f ∼ g as x→a); matrix similarity (∃ P invertible such that A = PBP⁻¹). |
| , , | — | — | First‑, second‑, n‑th derivative of a function f, i.e., f′, f″, f⁽ⁿ⁾. |
| 偏导符号 | Partial‑derivative symbol | — | Partial derivative with respect to a variable, e.g., ∂f/∂x. |
| 纳布拉算子 / 梯度符号 | Nabla operator | — | Gradient ∇f, divergence ∇·F, curl ∇×F. |
| 微分符号 | Differential symbol | — | Differential, e.g., dx, dy. |
| 积分符号 | Integral symbol | — | Indefinite integral ∫f(x)dx or definite integral ∫ₐᵇ f(x)dx. |
| / 二重 / 三重积分符号 | Double / Triple integral symbol | — | Double integral ∬ and triple integral ∭. |
| / 闭合曲线 / 曲面积分符号 | Closed line / surface integral symbol | — | Line integral over a closed curve ∮ and surface integral over a closed surface ∯. |
| 求和符号 | Sigma (summation symbol) | — | Summation, e.g., ∑_{i=1}^n a_i. |
| 泰勒余项 | Taylor remainder term | — | Remainder in a Taylor expansion (Peano or Lagrange form). |
| 近似等于符号 | Approximately equal to | — | Approximate equality, e.g., partial sums approximating the antiderivative. |
| （卷积）卷积符号 | Convolution symbol | — | Convolution operation, (f * g)(t) = ∫ f(τ)g(t‑τ)dτ. |
| 趋近符号 | Approaches | — | Variable approaching a value, e.g., x → 0⁺. |
| 矩阵 | Matrix A | — | Matrix (usually uppercase bold). |
| A 的转置 | Transpose of A | — | Transpose Aᵀ. |
| A 的逆矩阵 | Inverse of A | — | Inverse A⁻¹ satisfying AA⁻¹ = I. |
| 或 A 的共轭转置 | Conjugate transpose (Hermitian transpose) | — | Complex matrix conjugated then transposed, Aᴴ; for real matrices this coincides with the adjugate. |
| A 的伴随矩阵 | Adjugate matrix of A | — | Transpose of the cofactor matrix, adj A. |
| 或单位矩阵 | Identity/Unit matrix | — | Diagonal entries 1, all others 0. |
| 零矩阵 | Zero matrix | — | All entries are 0. |
| A 的秩 | Rank of A | — | Highest order of a non‑zero minor of A. |
| A 的迹 | Trace of A | — | Sum of diagonal entries. |
| 或 A 的行列式 | Determinant of A | — | Determinant |
| 向量 | Vector v | — | Vector (usually lowercase bold, e.g., column vector). |
| 点积符号 | Dot product symbol | — | Vector inner product, v·w. |
| 内积符号 | Inner product symbol | — | Inner product (real ⟨v,w⟩, complex ⟨v,w⟩). |
| 叉乘符号 | Cross product symbol | — | Cross product in ℝ³, v × w, yielding a vector orthogonal to both. |
| 向量范数符号 | Norm of vector v | — | Length (norm) of a vector, ‖v‖, e.g., ‖v‖ = √(v·v). |
| 线性变换 | Linear transformation T | — | Linear map sending space V to W. |
| T 的核 | Kernel of T | — | Set of vectors mapped to 0. |
| T 的像 | Image of T | — | Set of all outputs of T. |
| x 在基 B 下的坐标 | Coordinate vector of x | — | Column vector of coordinates of x relative to basis B. |
| 基 B 到 B' 的过渡矩阵 | Transition matrix | — | Matrix P satisfying [x]_{B'} = P[x]_B. |
| 或合同符号 | Congruent to | — | Matrix congruence (∃ P invertible such that A = PᵀBP). |
| 直和符号 | Direct sum symbol | — | Denotes that a space is a direct sum of subspaces, U ⊕ V. |
| 正交符号 | Orthogonal to | — | Vectors orthogonal (inner product 0) or orthogonal complement of a subspace. |
Common Greek Letter Symbols
| Symbol | Chinese Pronunciation | English Pronunciation | Meaning |
|---|---|---|---|
| (Alpha) | 阿尔法 | /ˈælfə/ (Alpha) | Calculus: parameter, angle, eigenvalue, objects for comparison tests. Linear algebra: abstract vector (e.g., α ∈ ℝⁿ). |
| (Beta) | 贝塔 | /ˈbiːtə/ (Beta) | Calculus: parameter, angle, eigenvalue, objects for comparison tests. Linear algebra: abstract vector (e.g., β). |
| (Gamma) | 伽马 | /ˈɡæmə/ (Gamma) | Calculus: Gamma function Γ(x). Linear algebra: often used as a placeholder parameter. |
| (Delta) | 德尔塔 | /ˈdeltə/ (Delta) | Calculus: difference Δx, Dirac delta δ(x). Linear algebra: placeholder parameter. |
| (Delta, uppercase) | 大写德尔塔 | /ˈdeltə/ (Delta) | Discriminant (e.g., quadratic Δ = b²‑4ac), finite‑difference operator. |
| (Epsilon) | 伊普西龙 | /ˈɛpsɪlɒn/ (Epsilon) | Calculus: arbitrarily small positive number (ε‑δ language), infinitesimal notation ε. |
| (Theta) | 西塔 | /ˈθiːtə/ (Theta) | Calculus: angle (radians), rotation parameter (polar coordinates, rotation matrices). |
| (Lambda) | 兰姆达 | /ˈlæmdə/ (Lambda) | Calculus: limit in root‑test, eigenvalue of differential equations. Linear algebra: eigenvalue of a matrix (λ). |
| (Mu) | 缪 | /mjuː/ (Mu) | Calculus: small coefficient, expectation (in probability extensions). Linear algebra: rarely used. |
| (Xi) | 克西 | /zaɪ/ (Xi) | Calculus: integration variable (e.g., ∫ f(ξ)dξ). Linear algebra: rarely used. |
| (Pi) | 派 | /paɪ/ (Pi) | Calculus: the constant π ≈ 3.14159. Linear algebra: placeholder parameter. |
| (Pi, uppercase) | 大写派 | /paɪ/ (Pi) | Calculus: product notation, ∏_{i=1}^n a_i. |
| (Rho) | 柔 | /roʊ/ (Rho) | Calculus: intermediate point in Taylor remainder, etc. Linear algebra: spectral radius ρ(A). |
| (Sigma) | 西格玛 | /ˈsɪɡmə/ (Sigma) | Calculus: standard deviation, perturbation amount, intermediate point in Taylor remainder. Linear algebra: singular value (SVD), element of a permutation group. |
| (Sigma, uppercase) | 大写西格玛 | /ˈsɪɡmə/ (Sigma) | Calculus / Linear algebra: summation symbol ∑. |
| (Tau) | 陶 | /tɔː/ (Tau) | Calculus: time variable, shear stress (physics extensions). Linear algebra: rarely used. |
| (Phi) | 斐 | /faɪ/ (Phi) | Calculus: potential function (gradient fields), auxiliary function. Linear algebra: linear transformation (Φ). |
| (Psi) | 普西 | /saɪ/ (Psi) | Calculus: auxiliary function (e.g., ψ in wave equations). Linear algebra: rarely used. |
| (Omega) | 欧米伽 | /oʊˈmeɡə/ (Omega) | Calculus: infinity (in extended sense), angular frequency (Fourier series). Linear algebra: rarely used. |
Originally written by Li Wei (李唯_) and published in Chinese on 后端技术栈全书 (Full-Stack Backend Engineering). Translated and adapted for DriftSeas with permission.