线性代数

Name: 线性代数
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Course

Chinese

4 h

Source

From www.xuetangx.com

More info

2 Sequences
Introductive Level
Starts on September 14, 2015
Ends on February 1, 2016

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Course details

Syllabus

线性代数导论: 线性代数导论; 评分标准; 建议学时分配

课程介绍: 课程介绍

行列式: 1-行列式概念的引进; 2-n阶行列式; 3-特殊行列式的计算; 4-行列式的性质; 5-行列式的计算; 6-克莱姆法则; 7-范德蒙行列式介绍; 逆序数与行列式; 行列式展开定理

矩阵: 1-矩阵是什么？; 2-几种特殊的矩阵; 3-矩阵运算-1; 4-矩阵运算-2; 5-方阵的行列式; 6-伴随矩阵; 7-初等变换; 8-矩阵的秩; 9-初等矩阵; 10-逆矩阵的定义及可逆条件; 11-逆矩阵的性质及求法2; 12-逆矩阵的求法3-4; 13-分块矩阵; 14-矩阵方程; 15-矩阵习题课; 矩阵一章习题; 讨论题

n维向量: 1-向量及其线性运算; 2-向量组的线性相关性; 3--相关性的判定定理; 4--相关性判定定理4与5的证明; 5--向量组的极大无关组与秩的定义; 6--向量组的极大无关组与秩的求法; 7--向量空间; 8--向量组的正交性; 9-向量组习题课; n维向量习题

线性方程组: 1--齐次方程组; 2--基础解系的求法; 3--非齐次方程组; 4--含参数的方程组; 5--方程组习题课; 6--与方程组有关的证明题

相似对角形: 1--矩阵的相似; 2--特征值与特征向量的求法; 3--特征值与特征向量的性质; 4--一般矩阵的相似对角形; 5--实对称矩阵特征值与特征向量的性质; 6--实对称矩阵的相似对角化; 7-相似对角形小结; 8-相似对角形习题课; 习题

二次型: 2--正交变化法化二次型为标准型; 3--配方法化二次型为标准型; 4--二次型的分类; 5-二次型习题课; 1-二次型及其矩阵

讨论区成绩: 讨论区成绩

Prerequisite

None.

Instructors

秦静

Platform

Founded by Tsinghua University in October 2013, XuetangX is the world’s first Chinese MOOC platform and serves as the research and application platform for the Ministry of Education (MOE) Research Center for Online Education. XuetangX has been awarded as one of the national first batch of demonstration base projects for innovation and entrepreneurship. Besides, XuetangX also works with the International Center for Engineering Education (ICEE) under the auspices of UNESCO and supports its online portion. By the end of June 2018, with a total of 25 million enrollments and more than 1,500 online courses from 13 disciplined fields, XuetangX has accumulated over 12 million registered users, covering 209 countries and regions.

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