线性代数专业 Certification
向量、矩阵与变换——数据科学、图形学与机器学习背后的数学基础
Key facts
- Level: Professional
- Field: Mathematics
- Estimated study time: about 32 hours
- Credential price: $149
- Exam: 88 questions · 140 minutes · pass mark 75%
About the 线性代数专业 certification
线性代数专业认证证明您能够流畅地运用向量、矩阵与线性变换进行推理——这是机器学习、计算机图形学、数据科学、工程学、量子力学与优化理论的数学引擎。 您将掌握向量与向量空间（向量运算、点积与叉积、范数与距离、线性组合与张成、子空间与向量空间公理）；线性方程组（高斯消元法、行最简形式、秩，以及判定方程组无解、有唯一解或无穷多解的相容性条件）；矩阵的完整代数运算（乘法、转置、逆矩阵，以及各类特殊矩阵——单位矩阵、对角矩阵、对称矩阵、正交矩阵、三角矩阵）；行列式（余子式展开、乘积性质与初等行变换性质，以及克拉默法则）；线性无关性、基与维数，以及由秩-零化度定理联结的四个基本子空间（列空间、零空间、行空间与左零空间）；线性变换（矩阵表示、核与像）；特征值与特征向量（特征多项式、对角化与相似性）；正交性（投影、格拉姆-施密特正交化过程与正交矩阵）；内积空间、谱定理，以及对称矩阵与正定矩阵；奇异值分解（SVD）入门；以及使这一切意义凸显的应用——最小二乘法、主成分分析（PCA）、马尔可夫矩阵和图形变换。 每个主题均以具体数值示例进行教学与考核——学完后您能够手动行化简方程组、计算逆矩阵与行列式、求特征值与特征向量、投影向量并运行格拉姆-施密特过程，并能读懂每个计算背后的几何含义。本认证以代数和预微积分为基础，是进入数据科学、机器学习与高级工程认证的自然跳板。
What you will learn
The official 线性代数专业 study course covers:
- Vectors & Vector Spaces — Vector operations, dot and cross products, norms, linear combinations, span and subspaces.
- Systems & Gaussian Elimination — Solving linear systems, row reduction to RREF, rank, and the consistency conditions.
- Matrices & Determinants — Matrix algebra, transpose and inverse, special matrices, and the determinant with its properties.
- Independence, Basis & the Four Subspaces — Linear independence, basis and dimension, and the four fundamental subspaces with rank-nullity.
- Transformations & Eigenvalues — Linear transformations and their matrices, kernel and image, eigenvalues, eigenvectors and diagonalisation.
- Orthogonality, Spectral Theorem & SVD — Projections, Gram-Schmidt, orthogonal matrices, the spectral theorem, SVD and real applications.
- 动手实验——向量、系统与特征值 — Google Colab 中的线性代数顶点项目：使用向量和投影进行计算，用矩阵和行列式求解系统，寻找特征值并观察变换，应用 SVD 压缩数据。纯 Python 与 NumPy，免费运行。
Prerequisites
Frequently asked questions
- Is the 线性代数专业 certificate verifiable?
- Yes. Every issued Hootix Academy certificate carries a unique credential code that anyone can verify online.
- How is the 线性代数专业 exam structured?
- It is a 140-minute proctored multiple-choice exam of 88 questions; you need 75% to pass.
- Do I need to buy the course to take the exam?
- You can purchase the certification exam on its own, or bundle it with the full study course at a reduced price.
- How long does the 线性代数专业 course take?
- About 32 hours of self-paced study.