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====== Proseminar: Functions of Matrices ====== | ====== Proseminar: Functions of Matrices ====== | ||
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+ | Probably the most well-known matrix function (or function of matrix) is the matrix exponential. | ||
+ | It is defined by inserting a matrix in the power series of the exponential function | ||
+ | $$e^A = \sum_{k=0}^\infty{1 \over k!}A^k.$$ | ||
+ | This raises the question: Can we define a matrix sine function by inserting a matrix in the power series of the scalar sine function? | ||
+ | The answer is yes: | ||
+ | $$ | ||
+ | \sin(A) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!}A^{2n+1}. | ||
+ | $$ | ||
+ | In this seminar, we will discuss when and how we can extend scalar functions to matrices, the properties of these functions and various applications. | ||
+ | |||
+ | |||
==== Registration ==== | ==== Registration ==== | ||
- | Please write a mail to [[:people |Alexander Zeilmann]] until October 20th, 2021 if you consider participating. | + | There are still topics available! |
+ | Please write a mail to [[:people |Alexander Zeilmann]], if you are interested. | ||
- | The first meeting, discussing the seminar and answering questions will take place in the first or second week of the semester. | + | The first meeting, discussing the seminar and answering questions will take place in the first week of the semester. |
Afterward, you write a mail with a ranking of your favorite 2 (or more) papers, that the papers can be assigned in case of collisions (otherwise chosen by lot). | Afterward, you write a mail with a ranking of your favorite 2 (or more) papers, that the papers can be assigned in case of collisions (otherwise chosen by lot). | ||
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* **Submission slides:** one week in advance of your presentation | * **Submission slides:** one week in advance of your presentation | ||
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* **Submission summary:** one week after your presentation | * **Submission summary:** one week after your presentation | ||
- | + | * **Talks:** weekly virtual seminar | |
- | * **Talks:** Depending on the number of participants as block seminar or weekly seminar. The seminar will be entirely online. | + | |
- | ==== Papers ==== | + | ==== Topics ==== |
- | Will be discussed in the preliminary meeting. | + | A few chapters from the book **Functions of Matrices** by Nicholas Higham. |