ETH Zurich Recap - Linear Algebra скачать в хорошем качестве

ETH Zurich Recap - Linear Algebra

This lecture recap distills the core ideas of linear algebra as taught at ETH Zurich, focusing on why the theory exists and how it is used in practice. The video begins with linear systems and the motivation behind linear algebra, then builds the full toolkit step by step. You’ll see how algebraic properties translate into computational methods, and how structure in matrices leads to efficient and stable algorithms. Topics covered: 00:00 Introduction & Motivation 02:28 Purpose of Linear Algebra & Linear Systems 13:10 Algebraic Rules & Matrix Properties 21:25 Solving Systems: Inverse, Cholesky (LDL), LU, QR, SVD 1:22:07 Vector Spaces 1:30:45 Matrix Properties: Norms, Orthogonality, Determinants 1:44:00 Eigenvalues & Eigenvectors 1:59:55 Special Matrices: Square, Symmetric, Normal, Orthogonal, Triangular, Diagonal, Nilpotent, Skew-Symmetric, Positive Definite, Idempotent 2:27:15 Covariance & Correlation Matrices This recap emphasizes intuition, structure, and connections—ideal for students, engineers, and anyone preparing for exams or applying linear algebra in data science, ML, or numerical computing.