-
Title: Selfadjoint and Unitary Matrices
-
Series: Linear Algebra
-
Chapter: Eigenvalues and similar things
-
YouTube-Title: Linear Algebra 60 | Selfadjoint and Unitary Matrices
-
Bright video: Watch on YouTube
-
Dark video: Watch on YouTube
-
Ad-free video: Watch Vimeo video
-
Original video for YT-Members (bright): Watch on YouTube
-
Original video for YT-Members (dark): Watch on YouTube
-
Forum: Ask a question in Mattermost
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: la60_sub_eng.srt missing
-
Download bright video: Link on Vimeo
-
Download dark video: Link on Vimeo
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $A \in \mathbb{C}^{n \times n}$ be given by the identity matrix. What is not correct?
A1: $A$ is skew-adjoint.
A2: $ A^* = A $.
A3: $A$ is unitary.
A4: $A$ is normal.
A5: $A^{-1} = A^\ast$.
Q2: Let $A \in \mathbb{C}^{2 \times 2}$ be given by $ \begin{pmatrix} i & 0 \ 0 & i\end{pmatrix}$. What is not correct?
A1: $A$ is selfadjoint.
A2: $A$ is skew-adjoint.
A3: $A$ is unitary.
A4: $A$ is normal.
A5: $A^{-1} = A^\ast$.
Q3: Let $A \in \mathbb{C}^{n \times n}$. What can you definitely say about the matrix $B$ given by $$ B = \frac{1}{2 i} ( A - A^\ast)$$
A1: $B$ is selfadjoint.
A2: $B$ is skew-adjoint.
A3: $B$ is unitary.
A4: $B$ only has real numbers as entries.
-
Last update: 2024-10
