【线性代数】MIT Linear Algebra Lecture 5: Transposes, permutations, spaces R^n

Author｜ Rickyの水果摊

Time ｜ 2022.9.11

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Lecture 5: Transposes, permutations, spaces $R^n$

Lecture Info

1. Instructor: Prof. Gilbert Strang

2. Course Number: 18.06

3. Topics: Linear Algebra

4. Official Lecture Resource: Resource Index of Linear Algebra

Excellent Notes on GitHub

There are some classic, excellent notes from other authors on GitHub, wihch I highly recommend you to star ⭐️ and read 📖

notes-linear-algebra (A systematic notes written in Chinese)

The-Art-of-Linear-Algebra (Focus on visualization of important concept of Linear Algebra)

Video Link

Lecture 5: Transposes, permutations, spaces $R^n$ (bilibili)

Lecture 5: Transposes, permutations, spaces $R^n$ (YouTube)

Key Points

1. Transposes and symmetric matrix
2. vector space
3. subspaces
4. column space - $C(A)$

Active Recall Questions

1. If $R$ is a rectangular matrix, then $N=R^T\ast R$ must be a symmetric matrix. Why?
2. What are the different types of vector space in general?
3. What are the basic rules that a vector space have to follow?
4. What are the properties that a vector in ${\mathbb{R}}^n$ have? (Hint: dimension of vectors & value type of each components)
5. List all the possible subspaces of ${\mathbb{R}}^n$
6. What’s the differences between ${\mathbb{R}}^2$ and a subspace (plane) of ${\mathbb{R}}^n$
7. List the vector sets of l i n e 1 : y = x , l i n e 2 : y = − x + 1 line1:y=x,line2:y=-x+1