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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-algebra-problem-based/
课程评论：没有评论
课程名称：线性代数：基于问题的学习方法 课程概述： 本课程的核心在于解决问题。学习本课程的最佳方式是提出问题，我将通过练习题来解答和拓展你的疑问。 课程内容涵盖： * **为何学习线性代数？** * **线性方程组与高斯消元法** * **矩阵：秩、迹与行列式** (这些是线性代数中的重要不变量) * **向量空间与子空间** * **基、维度、线性相关/无关、生成集与张成** * **重要的向量空间：** 矩阵的零空间、行空间和列空间、向量集的张成、向量空间的交集、和与直和、特征空间、正交补、线性变换的核与像 * **线性变换：** 线性变换的单射、满射、双射条件 * **矩阵与线性变换的关系：** 坐标、表示线性变换的矩阵 * **维度定理** (这是一项非常重要且强大的内容) * **特征值、特征向量与对角化** * **内积空间、范数、柯西-施瓦茨不等式、广义余弦定理** 本课程内容丰富且会定期更新，祝你学习愉快！
The focus of this course is on solving problems. Where the best way to benefit from the course is to ask questions and in hand I will respond with answers involving exercises that expand upon the questions. The topics covered are:Why Linear Algebra?Linear Systems of Equations, Gaussian EliminationMatricesRank, Trace and the Determinant of a matrix. These are important invariants in Linear AlgebraVector spaces and sub-vector spacesBasis, dimension, linear dependence/independence, spanning sets and spanImportant vector spaces: Null space of a matrix, row and column spaces of a matrix, Span of a set, intersection, sum and direct sum of vector spaces, eigenspace, orthogonal complement, Kernel and Image of a linear transformationLinear transformations. Conditions of a linear transformation to be injective, surjective, bijectiveRelation between matrices and linear transformations. Coordinates, Matrices representing a linear transformationDimension theorems - This is a very important and powerful topicEigenvalues, Eigenvectors and DiagonalizationInner product spaces, norms, Cauchy-Schwartz, general law of cosines - An inner product space is a vector space along with an inner product on that vector space. When we say that a vector space V is an inner product space, we are also thinking that an inner product on V is lurking nearby or is obvious from the contextThe course is highly dynamic and content is uploaded regularly.Happy Linear Algebra!
