MAST10007 精讲 Linear Algebra

大学：University of Melbourne

专业：MAST10007 Linear Algebra

授课方式：线上

开课时间：2021/03/02

$580

课程介绍:

了解掌握matrix, vector, system of equations的概念和方法了解抽象的vector spaces的概念掌握用matrix和vector的方法解决几何问题和实际问题的能力每周知识巩固精讲自编习题当堂练习

Lesson 01 Week 3：vector, line, plane的转换

Vector运算的几何意义 Line/plane的几种表达式及转换 Vector space的介绍

Lesson 02 Week 4：Subspace, linear (in)dependence, spanning set的证明

认识几种vector space Subspace的证明 Linear (in)dependence的证明 Spanning set的证明

Lesson 03 Week 5：span & basis of vector space

强化spanning set的概念 Vector space的basis和dimension的意义和特殊性质

Lesson 04 Week 6：column space, row space, solution space和rank-nullity theorem的联系

Column space, row space, solution space的计算如何串联起几个特殊值：Rank-nullity theorem Isomorphism的概念,转换几种vector space Linear transformation的证明 Linear transformation的代数运算和几何运算

Lesson 05 Week 7：Linear transformation的证明及计算 Image, kernel & nullity

Linear transformation强化及其matrix representation Image, kernel & nullity的联系和求法

Lesson 06 Week 8: Transition matrix & change of basis

Injective/surjective/invertible的判断 Transition matrix和Change of basis的求法介绍eigenvalue和eigenvector的概念

Lesson 07 Week 9: eigenvalue, eigen-vector的求法；diagonalisation的证明

Eigenvalue的求法：characteristic equation 用eigenvalue算det, trace Diagonalisation的概念和证明用diagonalisation来简化计算matrix power

Lesson 08 Week 10: inner product的证明； orthogonal set的概念

Inner product的概念和证明 Inner product on a complex vector space的证明：Hermitian inner product Inner product中的几何意义 Orthogonal set的概念从general basis求orthonormal basis

Lesson 09 Week 11: 用公式求orthogonal diago-nalization, unitary matrices, Hermitian matrices和least squares curve fitting

Orthogonal diagonalisation的求法步骤 Unitary matrices & Hermitian matri-ces的概念 Least squares curve fitting问题的通法

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