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Title: Inner Product and Norm
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Series: Linear Algebra
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Chapter: Vectors in $ \mathbb{R}^n $
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YouTube-Title: Linear Algebra 9 | Inner Product and Norm
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Bright video: https://youtu.be/SCTWQ_W1Cw8
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Dark video: https://youtu.be/fXWdBineqWI
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Ad-free video: Watch Vimeo video
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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: la09_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: Let $\mathbf{v},\mathbf{w} \in \mathbb{R}^3$ be given by $\mathbf{v} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}$ and $\mathbf{w} = \begin{pmatrix} -2 \ 1 \ 0 \end{pmatrix}$. Are the two vectors orthogonal?
A1: Yes!
A2: No!
Q2: Let $\mathbf{v} \in \mathbb{R}^4$ be given by $\mathbf{v} = \begin{pmatrix} 3 \ 4 \ 0 \ 1 \end{pmatrix}$. What is $| \mathbf{v} |$?
A1: 0
A2: 1
A3: 5
A4: $\sqrt{10}$
A5: $\sqrt{26}$
Q3: What is not a property of the standard inner product $\langle \cdot, \cdot \rangle : \mathbb{R}^n \times \mathbb{R}^n \rightarrow \mathbb{R}$?
A1: Positive definite
A2: Symmetric
A3: Linear in the second argument
A4: Linear in the first argument
A5: $\langle \mathbf{v}, \mathbf{v}\rangle = 0 ~ \Leftrightarrow ~ \mathbf{v}=0$
A6: $\langle \mathbf{v}, \mathbf{v}\rangle = 0 ~ \Leftrightarrow ~ \mathbf{v}\neq 0$
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Last update: 2024-10
