-
Title: Linear Subspaces
-
Series: Abstract Linear Algebra
-
Chapter: General vector spaces
-
YouTube-Title: Abstract Linear Algebra 3 | Linear Subspaces
-
Bright video: https://youtu.be/Ek5Ebm6t6nY
-
Dark video: https://youtu.be/d77TOcT_Eeo
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: ala03_sub_eng.srt missing
-
Timestamps
00:00 Introduction
00:36 Abstract vector space
01:38 Behaviour of the zero vector
03:00 Proof for the formulas
07:13 Linear subspaces = special vector spaces
10:00 Definition of linear subspace
12:02 Example quadratic polynomials
14:07 Credits
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $V$ be a vector space with zero vector $\mathbf{o}$. Which claim is correct?
A1: $0 \cdot v = \mathbf{o}$ for all $v \in V$.
A2: $(-1) \cdot v = \mathbf{o}$ for all $v \in V$.
A3: $\lambda \cdot v = \mathbf{o}$ for all $v \in V$ and all $\lambda \in \mathbb{F}$.
A4: $(-1) \cdot v + v = v$ for all $v \in V$.
Q2: Let $V$ be a vector space and $U \subseteq V$ a subspace. What is not correct in general?
A1: $u + v \in U$ for each $u \in U$ and $v \in V$.
A2: $u + v \in U$ for all $u,v \in U$.
A3: $\lambda \cdot u \in U$ for all $ u \in U$ and all $\lambda \in \mathbb{F}$.
A4: The zero vector lies in $U$.
-
Last update: 2024-10