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Title: Spectral Mapping Theorem
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Series: Linear Algebra
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Chapter: Eigenvalues and similar things
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YouTube-Title: Linear Algebra 63 | Spectral Mapping Theorem
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Bright video: https://youtu.be/KWGpLLHGr28
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Dark video: https://youtu.be/r9ZWx1NKNX0
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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: la63_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: Consider the matrix $\begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}$. What are the eigenvalues?
A1: $-i$ and $i$
A2: $-1$ and $1$
A3: $-i$ and $1$
A4: $-1$ and $i$
Q2: Consider the matrix $ A = \begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}$. What are the eigenvalues of the matrix $A^{10}$?
A1: Only $-1$
A2: $-1$ and $1$
A3: $-i$ and $1$
A4: Only $1$
A5: $0$ and $1$
Q3: Let $ A $ be a matrix with spectrum ${ 0, 1}$. Now consider the matrix $B = A^3 + 2 A^2 - 1$. What is correct?
A1: $\mathrm{spec}(B) = { -1, 2 } $
A2: $\mathrm{spec}(B) = { 0,1 } $
A3: $\mathrm{spec}(B) \subseteq { 0 } $
A4: $\mathrm{spec}(B) \supseteq { 0, 1} $
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Last update: 2024-10
