| linear combination |
线性组合 |
| scalar |
标量 |
| zero vector |
零向量 |
| dot product / inner product |
点积 / 内积 |
| outer product |
外积 |
| length / norm |
长度 / 范数 |
| Cauchy-Schwarz inequality |
Cauchy-Schwarz 不等式 |
| column space |
列空间 |
| row space |
行空间 |
| transpose |
转置 |
| dependent / independent |
线性相关 / 线性无关 |
| rank |
秩 |
| column rank / row rank |
列秩 / 行秩 |
| identity matrix |
单位矩阵 |
| zero matrix |
零矩阵 |
| triangular matrix |
三角矩阵 |
| orthogonal matrix |
正交矩阵 |
| matrix factorization |
矩阵分解 |
| elimination |
消元 |
| back substitution |
回代 |
| pivot |
主元 |
| augmented matrix |
增广矩阵 |
| invertible matrix |
可逆矩阵 |
| inverse matrix |
逆矩阵 |
| cofactor matrix |
余子式矩阵 |
| permutation matrix |
置换矩阵 |
| row exchange |
行交换 |
| lower triangular matrix |
下三角矩阵 |
| upper triangular matrix |
上三角矩阵 |
| symmetric matrix |
对称矩阵 |
| difference matrix |
差分矩阵 |
| cumulative sum matrix |
累加矩阵 |
| eigenvalue / eigenvector |
特征值 / 特征向量 |
| singular value / singular vector |
奇异值 / 奇异向量 |
| least squares |
最小二乘 |
| determinant |
行列式 |
| basis / dimension |
基 / 维数 |
| vector space / subspace |
向量空间 / 子空间 |
| span |
张成 |
| range / kernel |
值域 / 核 |
| nullspace |
零空间 |
| left nullspace |
左零空间 |
| reduced row echelon form (RREF) |
简化行阶梯形 |
| pivot column / free column |
主元列 / 自由列 |
| particular solution |
特解 |
| homogeneous equation |
齐次方程 |
| incidence matrix |
关联矩阵 |
| spanning tree |
生成树 |
| Kirchhoff’s laws |
Kirchhoff 定律 |
| pseudoinverse |
伪逆 |
| left inverse / right inverse |
左逆 / 右逆 |
| orthogonal projection |
正交投影 |
| orthogonal complement |
正交补 |
| direct sum |
直和 |
| projection matrix |
投影矩阵 |
| least squares approximation |
最小二乘近似 |
| regression |
回归 |
| normal equations |
正规方程 |
| conjugate transpose |
共轭转置 |
| Gram-Schmidt process |
Gram-Schmidt 正交化 |
| determinant |
行列式 |
| permutation parity |
置换的奇偶性 |
| minor |
子式 |
| cofactor |
余子式 |
| cofactor expansion / Laplace expansion |
余子子展开 / Laplace 展开 |
| Cramer’s rule |
Cramer 法则 |
| edge matrix |
边矩阵 |
| parallelogram / parallelepiped |
平行四边形 / 平行六面体 |
| oriented volume |
带方向体积 |
| characteristic equation |
特征方程 |
| algebraic multiplicity |
代数重数 |
| trace |
迹 |
| diagonalization |
对角化 |
| eigenvector matrix |
特征向量矩阵 |
| similar matrices |
相似矩阵 |
| spectral theorem |
谱定理 |
| positive definite / semidefinite |
正定 / 正半定 |
| quadratic form / energy |
二次型 / 能量 |
| leading principal minor |
顺序主子式 |
| generalized eigenvector |
广义特征向量 |
| matrix exponential |
矩阵指数 |
| centered difference |
中心差分 |
| second difference |
二阶差分 |
| mode shape |
振型 |
| singular value decomposition (SVD) |
奇异值分解 |
| left / right singular vector |
左 / 右奇异向量 |
| reduced / full SVD |
经济型 / 完整 SVD |
| spectral norm |
谱范数 |
| Frobenius norm |
Frobenius 范数 |
| low-rank approximation |
低秩近似 |
| Eckart-Young theorem |
Eckart-Young 定理 |
| principal component analysis (PCA) |
主成分分析 |
| sample covariance matrix |
样本协方差矩阵 |
| QR iteration |
QR 迭代 |
| bidiagonal matrix |
双对角矩阵 |
| Householder reflection |
Householder 反射 |
| polar decomposition |
极分解 |
| linear transformation |
线性变换 |
| composition of transformations |
变换的复合 |
| coordinate vector |
坐标向量 |
| change of basis |
换基 |
| derivative matrix |
微分矩阵 |
| integral matrix |
积分矩阵 |
| complex conjugate |
复共轭 |
| modulus / argument |
模 / 辐角 |
| Hermitian matrix |
Hermitian 矩阵 |
| unitary matrix |
酉矩阵 |
| conjugate transpose |
共轭转置 |
| root of unity |
单位根 |
| discrete Fourier transform (DFT) |
离散 Fourier 变换 |
| cyclic convolution |
循环卷积 |
| convolution theorem |
卷积定理 |
| fast Fourier transform (FFT) |
快速 Fourier 变换 |
| Cooley-Tukey algorithm |
Cooley-Tukey 算法 |
| rectified linear unit (ReLU) |
修正线性单元 |
| bias vector |
偏置向量 |
| loss function |
损失函数 |
| gradient descent |
梯度下降 |
| stochastic gradient descent (SGD) |
随机梯度下降 |
| mini-batch |
小批量 |
| learning rate |
学习率 |
| momentum |
动量 |
| convolutional neural network (CNN) |
卷积神经网络 |
| max pooling |
最大池化 |
| batch normalization |
批量归一化 |
| backpropagation |
反向传播 |
| automatic differentiation |
自动微分 |
| sample mean / expected value |
样本均值 / 期望 |
| sample variance / population variance |
样本方差 / 总体方差 |
| binomial distribution |
二项分布 |
| Poisson distribution |
Poisson 分布 |
| normal distribution |
正态分布 |
| central limit theorem |
中心极限定理 |
| covariance matrix |
协方差矩阵 |
| joint / marginal probability |
联合概率 / 边缘概率 |
| Markov inequality |
Markov 不等式 |
| Chebyshev inequality |
Chebyshev 不等式 |
| Chernoff bound |
Chernoff 界 |
| Markov chain |
Markov 链 |
| stationary distribution |
平稳分布 |
| Perron-Frobenius theorem |
Perron-Frobenius 定理 |
