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線性代數 | 台大開放式課程線上共學社群

natural-science

目標對象

本開放式課程線上共學社群使用的學習內容適合對於 線性代數 有興趣的學生或一般民眾。


學習目標

我們協助蒐集各種優質的跨領域閱讀和自主學習資源，節省教育工作者和學習者的寶貴時間和提高學習成效，同時提供學習者一個可以交流討論、社群共學，教學相長的優質學習空間。歡迎加入我們，一起分享你推薦的學習資源清單、自主學習計畫、問題交流討論和學習筆記，認識志同道合的學習夥伴和戰友，一起學習成長，一起打造你的跨領域閱讀和自主學習知識庫！


事前準備

具備基礎電腦網路操作和高中學科能力，準備電腦及網路並預留學習時間即可線上參與。鼓勵學員積極參與並遵守社群規範。


內容描述

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本學習社群採線上非同步方式進行，學習內容主要使用台大 電機系 蘇柏青 老師 臺大開放式課程 NTU OCW 教材 (CC BY-NC-SA 3.0 TW)，並額外規劃筆記共享及問題討論區幫助學員交流學習，只要有電腦和網路即可線上隨時隨地參與社群共學並組成學習讀書會。


目錄大綱

新手出發
1 社群共學進行方式
2 問題討論和共享筆記方式
課程內容
1 Basic Concepts on Matrices and Vectors (1)
2 Basic Concepts on Matrices and Vectors (2)
3 Basic Concepts on Matrices and Vectors (3)
4 Basic Concepts on Matrices and Vectors (4)
5 Basic Concepts on Matrices and Vectors (5)
6 System of Linear Equations (1)
7 System of Linear Equations (2)
8 Gaussian Elimination (1)
9 Gaussian Elimination (2)
10 The language of set theory
11 Span of a Set of Vectors (1)
12 Span of a Set of Vectors (2)
13 Linear Dependence and Linear Independence (1)
14 Linear Dependence and Linear Independence (2)
15 Matrix Multiplication
16 Invertibility and Elmentary Matrices
17 Column Correspondence Theorem
18 The Inverse of a Matrix (1)
19 The Inverse of a Matrix (2)
20 Linear Transformations and Matrices (1)
21 Linear Transformations and Matrices (2)
22 Composition and Invertibility of Linear Transformations (1)
23 Composition and Invertibility of Linear Transformations (2)
24 Determinants (1)
25 Determinants (2)
26 Subspaces and their properties
27 Basis and Dimension (1)
28 Basis and Dimension (2)
29 The Dimension of Subspaces associated with a Matrix
30 Coordinate Systems
31 Matrix Representations of Linear Operators
32 Eigenvalues, Eigenvectors, and Diagonalization
33 The Characteristic Polynomial (1)
34 The Characteristic Polynomial (2)
35 Diagonalization of Matrices (1)
36 Diagonalization of Matrices (2)
37 The Geometry of Vectors Dot Product (1)
38 The Geometry of Vectors Dot Product (2)
39 Orthogonal Vectors (1)
40 Orthogonal Vectors (2)
41 Orthogonal Projections (1)
42 Orthogonal Projections (2)
43 Least Squares Approximations and Orthogonal Projection Matrices
44 Orthogonal Matrices and Operators
45 Symmetric Matrices (1)
46 Symmetric Matrices (2)
47 Symmetric Matrices (3)
48 Symmetric Matrices (4)
49 Vector Spaces and Their Subspaces (1)
50 Vector Spaces and Their Subspaces (2)
51 Vector Spaces and Their Subspaces (3)
52 Vector Spaces and Their Subspaces (4)
53 Linear Transformation (1)
54 Linear Transformation (2)
55 Linear Transformation (3)
56 Basis and Dimension (1)
57 Basis and Dimension (2)
58 Basis and Dimension (3)
59 Matrix Representations of Linear Operators (1)
60 Matrix Representations of Linear Operators (2)
61 The Matrix Representations of the Inverse of an Invertible Linear Operator (1)
62 The Matrix Representations of the Inverse of an Invertible Linear Operator (2)
63 Eigenvalues and Eigenvectors of a Matrix Representations of a Linear Operator
64 Inner Product Spaces (1)
65 Inner Product Spaces (2)
66 Inner Product Spaces (3)
67 Inner Product Spaces (4)
68 Inner Product Spaces (5)

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