| 符号 | 含义 | 示例 |
|---|---|---|
| \(+\) | 加法 (Addition) | \(2 + 3 = 5\) |
| \(-\) | 减法 (Subtraction) | \(7 - 4 = 3\) |
| \(\times\) | 乘法 (Multiplication) | \(2 \times 3 = 6\) |
| \(\div\) | 除法 (Division) | \(6 \div 2 = 3\) |
| \(\%\) | 百分比 (Percentage) | \(25\% \text{ of } 80 = 20\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(=\) | 等于 (Equal to) | \(5 = 5\) |
| \(\neq\) | 不等于 (Not equal to) | \(4 \neq 5\) |
| \(<\) | 小于 (Less than) | \(3 < 5\) |
| \(>\) | 大于 (Greater than) | \(7 > 5\) |
| \(\leq\) | 小于或等于 (Less than or equal to) | \(3 \leq 3\) |
| \(\geq\) | 大于或等于 (Greater than or equal to) | \(5 \geq 5\) |
| \(\approx\) | 约等于 (Approximately equal to) | \(\pi \approx 3.14\) |
| \(\equiv\) | 恒等于 (Identical to) | \(x \equiv x\) |
| \(\sim\) | 相似于 (Similar to) | \(\triangle ABC \sim \triangle DEF\) |
| \(\propto\) | 正比于 (Proportional to) | \(y \propto x\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\in\) | 属于 (Element of) | \(2 \in \mathbb{Z}\) |
| \(\notin\) | 不属于 (Not an element of) | \(\pi \notin \mathbb{Q}\) |
| \(\ni\) | 包含 (Contains as an element) | \(\mathbb{R} \ni \pi\) |
| \(\subset\) | 真子集 (Proper subset) | \(\{1,2\} \subset \{1,2,3\}\) |
| \(\subseteq\) | 子集 (Subset) | \(\{1,2\} \subseteq \{1,2,3\}\) |
| \(\supset\) | 真超集 (Proper superset) | \(\{1,2,3\} \supset \{1,2\}\) |
| \(\supseteq\) | 超集 (Superset) | \(\{1,2,3\} \supseteq \{1,2\}\) |
| \(\cup\) | 并集 (Union) | \(A \cup B\) |
| \(\cap\) | 交集 (Intersection) | \(A \cap B\) |
| \(\setminus\) | 差集 (Set difference) | \(A \setminus B\) |
| \(\emptyset\) | 空集 (Empty set) | \(\{x \in \mathbb{N} : x < 0\} = \emptyset\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\wedge\) | 与 (And) | \(p \wedge q\) |
| \(\vee\) | 或 (Or) | \(p \vee q\) |
| \(\neg\) | 非 (Not) | \(\neg p\) |
| \(\Rightarrow\) | 蕴含 (Implies) | \(p \Rightarrow q\) |
| \(\Leftrightarrow\) | 当且仅当 (If and only if) | \(p \Leftrightarrow q\) |
| \(\forall\) | 任意 (For all) | \(\forall x \in \mathbb{R}\) |
| \(\exists\) | 存在 (There exists) | \(\exists x \in \mathbb{R}\) |
| \(\therefore\) | 所以 (Therefore) | \(A=B, B=C, \therefore A=C\) |
| \(\because\) | 因为 (Because) | \(\because A=B \text{ and } B=C, \therefore A=C\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\angle\) | 角 (Angle) | \(\angle ABC\) |
| \(\perp\) | 垂直 (Perpendicular) | \(l_1 \perp l_2\) |
| \(\parallel\) | 平行 (Parallel) | \(l_1 \parallel l_2\) |
| \(\cong\) | 全等 (Congruent) | \(\triangle ABC \cong \triangle DEF\) |
| \(\sim\) | 相似 (Similar) | \(\triangle ABC \sim \triangle DEF\) |
| \(\triangle\) | 三角形 (Triangle) | \(\triangle ABC\) |
| \(\square\) | 正方形 (Square) | \(\square ABCD\) |
| \(\circ\) | 度 (Degree) | \(90^\circ\) |
| \(\pi\) | 圆周率 (Pi) | \(\pi r^2\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\int\) | 积分 (Integral) | \(\int_a^b f(x) dx\) |
| \(\oint\) | 环路积分 (Contour integral) | \(\oint_C f(z) dz\) |
| \(\partial\) | 偏导数 (Partial derivative) | \(\frac{\partial f}{\partial x}\) |
| \(\nabla\) | 梯度 (Gradient) | \(\nabla f\) |
| \(\lim\) | 极限 (Limit) | \(\lim_{x \to \infty} f(x)\) |
| \(\sum\) | 求和 (Summation) | \(\sum_{i=1}^n i\) |
| \(\prod\) | 求积 (Product) | \(\prod_{i=1}^n i\) |
| \(\frac{d}{dx}\) | 导数 (Derivative) | \(\frac{d}{dx} f(x)\) |
| \(\iint\) | 二重积分 (Double integral) | \(\iint_D f(x, y) dx dy\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\sqrt{}\) | 平方根 (Square root) | \(\sqrt{4} = 2\) |
| \(\sqrt[n]{}\) | n次方根 (nth root) | \(\sqrt[3]{8} = 2\) |
| \(\|x\|\) | 绝对值 (Absolute value) | \(\|-5\| = 5\) |
| \(n!\) | 阶乘 (Factorial) | \(5! = 120\) |
| \(\binom{n}{k}\) | 二项式系数 (Binomial coefficient) | \(\binom{5}{2} = 10\) |
| \(\oplus\) | 异或 (Exclusive or) | \(1 \oplus 1 = 0\) |
| \(\otimes\) | 克罗内克积 (Kronecker product) | \(A \otimes B\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\mid\) | 整除 (Divides) | \(3 \mid 9\) |
| \(\nmid\) | 不整除 (Does not divide) | \(3 \nmid 10\) |
| \(\pmod{}\) | 取模运算 (Modulo operation) | \(7 \pmod{3} \equiv 1\) |
| \(\gcd\) | 最大公约数 (Greatest common divisor) | \(\gcd(12,18) = 6\) |
| \(\text{lcm}\) | 最小公倍数 (Least common multiple) | \(\text{lcm}(4,6) = 12\) |
| \(\infty\) | 无穷大 (Infinity) | \(\lim_{x \to 0} \frac{1}{x} = \infty\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\det\) | 行列式 (Determinant) | \(\det(A)\) |
| \(\text{tr}\) | 矩阵的迹 (Trace of a matrix) | \(\text{tr}(A)\) |
| \(A^T\) | 矩阵转置 (Matrix transpose) | \((A^T)_{ij} = A_{ji}\) |
| \(A^{-1}\) | 矩阵逆 (Matrix inverse) | \(AA^{-1} = I\) |
| \(\ker\) | 核 (Kernel) | \(\ker(T)\) |
| \(\text{Im}\) | 像 (Image) | \(\text{Im}(T)\) |
| \(\text{rank}\) | 秩 (Rank) | \(\text{rank}(A)\) |
| \(\dim\) | 维数 (Dimension) | \(\dim(V)\) |
| \(\text{span}\) | 张成 (Span) | \(\text{span}\{v_1, v_2, \ldots, v_n\}\) |
| \(\cdot\) | 点积 (Dot product) | \(\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3\) |
| \(\times\) | 叉积 (Cross product) | \(\mathbf{a} \times \mathbf{b} = (a_2 b_3 - a_3 b_2, a_3 b_1 - a_1 b_3, a_1 b_2 - a_2 b_1)\) |
| \(\otimes\) | 克罗内克积 (Kronecker product) | \(A \otimes B\) |
| \(\mathbf{0}\) | 零向量 (Zero vector) | \(\mathbf{0} = (0, 0, \ldots, 0)\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(i\) | 虚数单位 (Imaginary unit) | \(i^2 = -1\) |
| \(z^*\) | 复共轭 (Complex conjugate) | \((a+bi)^* = a-bi\) |
| \(\|z\|\) | 模 (Modulus) | \(\|3+4i\| = 5\) |
| \(\arg(z)\) | 辐角 (Argument) | \(\arg(1+i) = \frac{\pi}{4}\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\mu\) | 总体均值 (Population mean) | \(\mu = \frac{1}{N}\sum_{i=1}^N x_i\) |
| \(\sigma\) | 标准差 (Standard deviation) | \(\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^N (x_i - \mu)^2}\) |
| \(\sigma^2\) | 方差 (Variance) | \(\sigma^2 = \frac{1}{N}\sum_{i=1}^N (x_i - \mu)^2\) |
| \(\rho\) | 相关系数 (Correlation coefficient) | \(-1 \leq \rho \leq 1\) |
| \(\chi^2\) | 卡方 (Chi-squared) | \(\chi^2 = \sum \frac{(O-E)^2}{E}\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(e\) | 欧拉数 (Euler's number) | \(\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e\) |
| \(\pi\) | 圆周率 (Pi) | \(\pi \approx 3.14159\) |
| \(i\) | 虚数单位 (Imaginary unit) | \(i^2 = -1\) |
| \(\gamma\) | 欧拉-马斯克若尼常数 (Euler-Mascheroni constant) | \(\gamma \approx 0.57721\) |
| \(\phi\) | 黄金比例 (Golden ratio) | \(\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618\) |
| \(\zeta(3)\) | 阿佩里常数 (Apéry's constant) | \(\zeta(3) = \sum_{n=1}^{\infty} \frac{1}{n^3} \approx 1.20206\) |
| \(\ln(2)\) | 2的自然对数 (Natural logarithm of 2) | \(\ln(2) \approx 0.69315\) |
| 符号 | 含义 | 示例 |
|---|---|---|
| \(\nabla\) | 梯度、散度或旋度 (Gradient, divergence, or curl) | \(\nabla f\) |
| \(\Box\) | 证明完毕 (End of proof) | \(\therefore x = 2 \quad \Box\) |
| \(\sim\) | 服从分布 (Distributed as) | \(X \sim N(\mu, \sigma^2)\) |
| \(\asymp\) | 渐近等价 (Asymptotically equivalent) | \(f(x) \asymp g(x)\) |
| \(\ll\) | 远小于 (Much less than) | \(1 \ll 1000\) |
| \(\gg\) | 远大于 (Much greater than) | \(1000 \gg 1\) |
| \(\to\) | 趋向于 (Tends to) | \(x \to \infty\) |
| \(\mapsto\) | 映射到 (Maps to) | \(f: x \mapsto x^2\) |
| 小写符号 | 大写符号 | 读音 | 含义 | 示例 |
|---|---|---|---|---|
| \(\alpha\) | \(A\) | 阿尔法 | 角度、系数 | \(\alpha = 45^\circ\) |
| \(\beta\) | \(B\) | 贝塔 | 角度、系数 | \(\beta = 0.5\) |
| \(\gamma\) | \(\Gamma\) | 伽马 | 伽马函数 | \(\Gamma(x)\) |
| \(\delta\) | \(\Delta\) | 德尔塔 | 德尔塔函数、变化量 | \(\Delta x = x_2 - x_1\) |
| \(\epsilon\) | \(E\) | 艾普西龙 | 微小量、介电常数 | \(\epsilon > 0\) |
| \(\zeta\) | \(Z\) | 泽塔 | 泽塔函数 | \(\zeta(s)\) |
| \(\eta\) | \(H\) | 伊塔 | 效率、粘度 | \(\eta = 0.8\) |
| \(\theta\) | \(\Theta\) | 西塔 | 角度 | \(\theta = 30^\circ\) |
| \(\iota\) | \(\iota\) | 约塔 | 微小量、索引 | \(\iota_n\) |
| \(\kappa\) | \(K\) | 卡帕 | 曲率 | \(\kappa = \frac{1}{R}\) |
| \(\lambda\) | \(\Lambda\) | 兰姆达 | 特征值、波长 | \(\lambda = 500 \, \text{nm}\) |
| \(\mu\) | \(M\) | 缪 | 均值、磁矩 | \(\mu = 10\) |
| \(\nu\) | \(N\) | 纽 | 频率 | \(\nu = 60 \, \text{Hz}\) |
| \(\xi\) | \(\Xi\) | 克西 | 随机变量 | \(\xi \sim N(0, 1)\) |
| \(o\) | \(O\) | 奥密克戎 | 奥密克戎 | \(o(n)\) |
| \(\pi\) | \(\Pi\) | 派 | 圆周率、乘积 | \(\pi \approx 3.14\) |
| \(\rho\) | \(P\) | 柔 | 密度、电阻率 | \(\rho = 1000 \, \text{kg/m}^3\) |
| \(\sigma\) | \(\Sigma\) | 西格玛 | 标准差、求和 | \(\sigma = 2\) |
| \(\tau\) | \(T\) | 陶 | 陶、力矩 | \(\tau = 5 \, \text{Nm}\) |
| \(\upsilon\) | \(\Upsilon\) | 宇普西龙 | 宇普西龙 | \(\Upsilon(x)\) |
| \(\phi\) | \(\Phi\) | 斐 | 斐、电势 | \(\phi = 10 \, \text{V}\) |
| \(\chi\) | \(X\) | 卡 | 卡、卡方 | \(\chi^2\) |
| \(\psi\) | \(\Psi\) | 普西 | 普西、波函数 | \(\Psi(x, t)\) |
| \(\omega\) | \(\Omega\) | 欧米伽 | 欧米伽、角频率 | \(\omega = 2\pi f\) |