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Title: Geometric Multiplicity
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Series: Linear Algebra
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Chapter: Eigenvalues and similar things
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YouTube-Title: Linear Algebra 56 | Geometric Multiplicity
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Bright video: https://youtu.be/BBcjHvCXJo0
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Dark video: https://youtu.be/-RlcgJ5K82k
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): https://youtu.be/Pn3K2wSDc1k
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Original video for YT-Members (dark): https://youtu.be/qcuDtwu_zL4
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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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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la56_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 $A \in \mathbb{R}^{3 \times 3}$ be a square matrix with $$ A = \begin{pmatrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 \end{pmatrix} $$ What is geometric multiplicity of the eigenvalue $2$?
A1: 3
A2: 0
A3: 1
A4: 2
Q2: Let $A \in \mathbb{R}^{3 \times 3}$ be a square matrix with $$ A = \begin{pmatrix} 2 & 1 & 1 \ 0 & 2 & 1 \ 0 & 0 & 2 \end{pmatrix} $$ What is geometric multiplicity of the eigenvalue $2$?
A1: 1
A2: 0
A3: 3
A4: 2
Q3: Let $A \in \mathbb{R}^{2 \times 2}$ with eigenvalue $5$ and $7$. Which of the following claims for the geometric multiplicity is the only possible one?
A1: $\gamma(5) = \gamma(7) = 1$
A2: $\gamma(5) + \gamma(7) = 1$
A3: $\gamma(5) + \gamma(7) = 3$
A4: $\gamma(5) = 2$
A5: $\gamma(7) = 0$
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Last update: 2024-10
