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Title: Eigenvalues and Eigenvectors
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Series: Linear Algebra
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Chapter: Eigenvalues and similar things
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YouTube-Title: Linear Algebra 53 | Eigenvalues and Eigenvectors
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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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: la53_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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Definitions in the video: eigenvalue, eigenvector, eigenspace, spectrum
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $A \in \mathbb{R}^{n \times n}$ be a square matrix. Is there a vector such that the equation $A \mathbf{x} = 3 \mathbf{x}$ is satisfied?
A1: Yes, there is at least one.
A2: No, there is never such a vector.
A3: Yes, there is always excatly one vector for this.
A4: One needs more information.
Q2: Let $A \in \mathbb{R}^{n \times n}$ be a square matrix. If there is a vector $\mathbf{x} \neq 0$ such that the equation $A \mathbf{x} = 3 \mathbf{x}$ is satisfied, what are to correct names?
A1: $3$ is called an eigenvalue of $A$ and $x$ an eigenvector.
A2: $3$ is called an eigenvector of $A$ and $x$ an eigenvalue.
A3: $3$ is called an eigenspace of $A$ and $x$ an eigenvalue.
A4: $3$ is called a scalar of $A$ and $x$ an eigenvalue.
Q3: Let $A \in \mathbb{R}^{2 \times 2}$ be a square matrix given by $\begin{pmatrix} 2 & 1 \ 0 & 3 \end{pmatrix}$. Try finding the eigenvaluas similarly to the procedure in the video. What is the spectrum of $A$?
A1: ${ 2,3 }$
A2: ${ 1, 2,3 }$
A3: ${ 0, 1, 2,3 }$
A4: ${ 1}$
A5: ${ 0 }$
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Last update: 2024-10
