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Title: Adjoint
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Series: Linear Algebra
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Chapter: Eigenvalues and similar things
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YouTube-Title: Linear Algebra 59 | Adjoint
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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: la59_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: adjoint matrix, conjugate transpose, Hermitian conjugate
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $A \in \mathbb{C}^{n \times m}$ but each entry is actually a real number. What is always correct?
A1: $ A^* = A^T $
A2: $ A^* = A $
A3: $ A^* = - A^T $
A4: $ A^* = - A $
Q2: Consider the vector space $\mathbb{C}^2$ with the standard inner product $\langle \cdot, \cdot \rangle$. What is correct?
A1: $ \langle x, y \rangle = x^\ast y $
A2: $ \langle x, y \rangle = x^T y $
A3: $ \langle x, y \rangle = x y $
A4: $ \langle x, A y \rangle = x A^\ast y $
A5: $ \langle x, y \rangle = y -x $
Q3: Consider the a matrix $A \in \mathbb{C}^{n \times n}$ with spectrum given by $i, 1, 2, e^i$. What is the spectrum of the adjoint $A^\ast$?
A1: ${ - i, 1, 2, e^{-i} }$
A2: ${ 1, 2 }$
A3: ${ i, 1, 2, e^{i} }$
A4: ${ 0 }$
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Last update: 2024-10
