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Title: Linear Maps (Definition)
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Series: Linear Algebra
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Chapter: Matrices and linear systems
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YouTube-Title: Linear Algebra 18 | Linear Maps (Definition)
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Bright video: https://youtu.be/l5jqJvQ2tA0
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Dark video: https://youtu.be/sST_bx4ZZRs
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): https://youtu.be/Xi-HknrH6OM
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Original video for YT-Members (dark): https://youtu.be/lJnwwbwPE-8
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la18_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What is not a property of a linear map $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$?
A1: $f( \mathbf{x} \cdot \mathbf{y} ) = f( \mathbf{x} ) \cdot f( \mathbf{y} ) $
A2: $f( \mathbf{x} + \mathbf{y} ) = f( \mathbf{x} ) + f( \mathbf{y} ) $
A3: $f( \lambda \mathbf{x}) = \lambda f( \mathbf{x} )$
A4: $f( \mathbf{x} + \lambda \mathbf{y} ) = f( \mathbf{x} ) + \lambda f( \mathbf{y} ) $
Q2: Let consider the vector space $X = \mathbb{R}$ and a map $f : X \rightarrow X$. Which of the statements is not correct?
A1: $f(x) = x^2$ is linear.
A2: $f(x) = x$ is linear.
A3: $f(x) = 2 x$ is linear.
A4: $f(x) = 3 x$ is linear.
A5: $f(x) = 0$ is linear.
Q3: Let consider the zero vector space $X = {0}$ and a map $f : X \rightarrow X$. Which of the statements is not correct?
A1: There is a map $f : X \rightarrow X$ that is not linear.
A2: $f(x) = x^2$ is linear.
A3: $f(x) = x$ is linear.
A4: $f(x) = 3 x$ is linear.
A5: $f(x) = 0$ is linear.
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Last update: 2024-10
