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Title: Singular Values and Singular Vectors
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Series: Abstract Linear Algebra
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Chapter: Some matrix decompositions
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YouTube-Title: Abstract Linear Algebra 50 | Singular Values and Singular Vectors
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Bright video: Watch on YouTube
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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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Subtitle on GitHub: ala50_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 $A \in \mathbb{C}^{m \times n}$. What is not correct for the singular values $s_i$ of $A$?
A1: Same singular values could lie in $\mathbb{C} \setminus \mathbb{R}$.
A2: We have $n$ singular values.
A3: The singular values are non-negatives.
A4: Same singular values can be zero.
Q2: Let $A \in \mathbb{C}^{m \times n}$. What is always correct for a right-singular vectors of $A$?
A1: It’s an eigenvector of $A^\ast A$.
A2: It’s a vector in $\mathrm{Ker}(A)$.
A3: It’s a vector in $\mathrm{Ran}(A)$.
A4: It’s an eigenvector of $A A^\ast$.
A5: It’s an eigenvector of $A$.
A6: It lies in $\mathrm{Ker}(A^\ast)$.
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Date of video: 2025-04-28
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Last update: 2025-10
