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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-algebra-part-4-echelon-matrix-normal-form-matrix/
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**课程名称：** 线性代数（四）：向量空间与子空间 **课程概述：** 本课程是线性代数系列的一部分，专注于向量空间、子空间及其相关概念。课程时长约为3小时54分钟，包含了关于行阶梯形矩阵、矩阵的行/列变换、矩阵秩、矩阵的标准型以及判断非奇异矩阵等一系列重要内容。 **课程内容要点：** * **行阶梯形矩阵：** 介绍行阶梯形矩阵的定义及相关示例。 * **子空间的基与维度：** 学习如何求解子空间的基和维度。 * **子空间和与交：** 掌握如何求解两个子空间的和与交的基以及维度。 * **特定向量集作为子空间：** 探讨向量集为矩阵、次数小于等于3的实系数多项式（包含零多项式）、xy平面、x轴等作为子空间时的基与维度求解。 * **秩的确定：** 结合子空间和与交的概念，学习确定矩阵的秩。 * **矩阵的行/列变换：** 探讨行/列变换在矩阵操作中的等价性。 * **矩阵标准型：** 引入矩阵标准型概念并提供示例。 * **通过标准型确定矩阵秩：** 学习如何通过将矩阵化为其标准型来确定其秩。 * **非奇异矩阵的确定：** 学习如何通过将矩阵A化为其标准型PAQ，从而确定非奇异矩阵P和Q。 **课程特色：** 课程包含所有重要的定理及其证明，并辅以大量已解示例、作业和练习题。
Linear Algebra, mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations. In this 3hr 54 min Course ' Linear Algebra Part 4 Echelon Matrix and Normal Form of Matrix' is having very interesting contents based on Echelon Matrix, Row Column Operations on matrix, Rank of Matrix, Normal Form of Matrix, and Determining the Non singular Matrices.The listed Contents of the Course 'Echelon Matrix & Normal Form of Matrix'1) The introduction to the Echelon Matrix and its definition with examples.2) Finding the Basis and Dimension of subspaces.3) Finding basis and dimension of the sum of subspaces.4) Finding the basis and dimension of intersection of subspaces.5) Finding the basis and dimension of subspaces having vectors as matrices.6) Finding the basis and dimension of subspaces having vectors as real polynomials of degree less than equal to 3 including the zero polynomial.7) Finding the basis and dimension of subspaces, having vectors as xy-plane or x axis or respective other axis and planes.8) Finding the basis and dimension of subspaces, sum of subspaces, intersection of subspaces with determination of rank too.9) Equivalence of row column operations on matrices.10) Normal form of matrix introduction with examples11) Determining the rank of matrix by reducing the given matrix into its normal form.12)Determining the non singular matrices P and Q by reducing the given matrix into its normal form such that PAQ is in normal form where A is the given matrix.Including all Important Theorems and Proofs with Solved Examples and assignments plus Practice Questions.
