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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-algebra-part-3-row-space-column-space-of-matrix/
课程评论：没有评论
**课程名称:** 线性代数第三部分：向量空间与矩阵秩 **课程概述:** 本课程时长为5小时23分钟，主要介绍了矩阵的行空间和行秩。课程内容包括： * **行前导元素和列索引的概念** * **行阶梯形矩阵的定义及其性质** * **行阶梯形矩阵的示例，以及初等行变换和初等列变换的定义** * **将矩阵化为行阶梯形矩阵的方法** * **从给定矩阵得到列阶梯形矩阵的方法** * **行空间和矩阵行秩的定义** * **列空间和矩阵列秩的定义** * **关于行空间和行秩的定理** * **关于列空间和列秩的定理** * **关于矩阵行空间和列空间的等价命题** * **求矩阵行空间的基和维数** * **求矩阵列空间的基和维数** * **由多项式生成的向量空间的基** * **由矩阵生成的向量空间的基** * **相对于标准基的坐标向量概念及求解实例** * **利用坐标向量求给定多项式或矩阵所生成向量空间的基** * **关于基和维数的作业，涵盖所有预期定理和各类示例** **教学大纲:** 无
Introducing this 5 hour 23 minute Course on ROW SPACE AND ROW RANK OF MATRIX The Course includes_The concepts of leading entries of rows and column indices.The definition for Row Echelon Matrix and its properties.The examples of Row Echelon Matrices and definition of Elementary Row Operations and Elementary Column Operations.Methods of reducing a matrix into row echelon formTo get Column echelon form matrix from given matrix.Definition of Row Space and Row rank of matrix.Definition of Column Space and Column Rank of matrix.Theorems on Row space and row rank of matrix.Theorems on Column space and column rank of matrix.The equivalent statements on matrices for row space and column space of matrixTo get Basis and Dimension of row space of matrix and To get Basis and Dimension of column space of matrix.Basis for the vector space generated by Polynomials.Basis for the vector space generated by matrices.Concept of Coordinate Vectors relative to standard basis and Solved Examples.And, To get Basis for vector space generated by given polynomials or matrices using Coordinate vectors.Assignments on Basis and Dimensions including all the Expected theorems and all types of examples based on the above contents.Thank You
