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Title: Diagonalizable Matrices
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Series: Linear Algebra
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Chapter: Eigenvalues and similar things
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YouTube-Title: Linear Algebra 65 | Diagonalizable Matrices
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Bright video: https://youtu.be/tDV9aENIkTc
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Dark video: https://youtu.be/PSbPuQDPg-I
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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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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la65_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 $A \in \mathbb{C}^{n \times n}$ with $2,4,6, \ldots, 2n$ as eigenvalues. Is $A$ diagonalizable?
A1: Yes, it is.
A2: No, it’s never diagonalizable.
A3: One needs more information.
Q2: Let $A \in \mathbb{C}^{2 \times 2}$ where $1$ is the only eigenvalue. Assume $A$ is diagonalizable. What is also correct?
A1: The geometric multiplicity of the eigenvalue $1$ is exactly 2.
A2: The algebraic multiplicity of the eigenvalue $1$ is 1.
A3: $A$ has $1$ and $2$ on the diagonal.
Q3: Let $A \in \mathbb{C}^{3 \times 3}$ be not diagonalizable. What is a correct conclusion?
A1: $A$ is not normal.
A2: $A$ has $3$ different eigenvalues.
A3: $A$ has only one eigenvalue.
A4: There is no eigenspace with dimension $2$.
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Last update: 2024-10
