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teaching:wt2122:proseminar [2021/09/16 16:46] ipa |
teaching:wt2122:proseminar [2021/10/27 13:37] (current) ipa |
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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 | ||
| + | eA=∞∑k=01k!Ak. | ||
| + | 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. | ||
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| ==== 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 | ||
| * **Submission summary:** one week after your presentation | * **Submission summary:** one week after your presentation | ||
| - | * **Talks:** Depending on the number of participants as block seminar or weekly seminar. Also depending on the current regulations and the wishes of the participants, the seminar will be in person or online. | + | * **Talks:** weekly virtual seminar |
| - | ==== Papers ==== | + | ==== Topics ==== |
| - | Will be discussed in the preliminary meeting. | + | A few chapters from the book **Functions of Matrices** by Nicholas Higham. |