Linear Algebra | Khan Academy
Learn linear algebra—vectors, matrices, transformations, and more.
概览
收录于
2026年3月17日
学科与领域
computer-science-advanced · computer-graphics
年级范围
九年级（高一）–十二年级（高四）
页面类型
Course
简介
Khan Academy: Linear Algebra Course Curriculum
- Vectors: Covers linear dependence/independence, dot and cross products, Cauchy-Schwarz inequality, vector triangle inequality, and geometric applications (planes, distances, and normal vectors).
- Matrices and Systems: Focuses on solving systems via elimination, null space, column space, basis, rank, and nullity.
- Linear Transformations: Explores functions as transformations, matrix-vector products, image/preimage, kernel, and the properties of linear transformation operations.
- Inverses and Determinants: Discusses invertibility, surjective/injective functions, the solution set of $Ax=b$, and methods for finding inverses.
- Orthogonality: Covers orthogonal complements, projections onto subspaces, least squares approximation, and orthonormal bases.
- Gram-Schmidt Process: Details the algorithm for constructing orthonormal bases and the properties of orthogonal matrices (preserving angles and lengths).
- Eigen-everything: Introduces eigenvalues and eigenvectors, including calculations for 2x2 and 3x3 matrices, eigenspaces, and the utility of eigenbases for coordinate systems.
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