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Title: Singular Value Decomposition (Algorithm and Example)
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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 51 | Singular Value Decomposition (Algorithm and Example)
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: ala51_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $A \in \mathbb{C}^{5 \times 2}$. What is the first step for determining the singular value decomposition of $A$ if you want to be efficient?
A1: Calculate the eigenvalues of $A^{\ast} A$.
A2: Calculate the eigenvalues of $A A^{\ast}$.
A3: Calculate the eigenvalues of $A^{\ast}$.
A4: Calculate the eigenvalues of $A$.
Q2: Let $A \in \mathbb{C}^{5 \times 2}$. What is correct for the vectors in $V$ and the vectors in $U$?
A1: We have 2 vectors $(v_1, v_2)$ and 5 vectors $(u_1, u_2, u_3, u_4, u_5)$.
A2: Most $u_j$ are equal to zero.
A3: There are 5 vectors $(v_1, v_2, v_3, v_4, v_5)$ and their are eigenvectors of $A^\ast A$.
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Date of video: 2025-04-30
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Last update: 2025-10
