# Independent study for linear algebra

1. Aug 3, 2016

### icesalmon

Hello, I just completed a first course in linear algebra and really enjoyed my studies. So much so that I want to pursue it more in the fall as an independent study, i am a EE major in college and was curious what directions might be useful for applications in that field.

2. Aug 3, 2016

### Lucas SV

Although I am a phycisist, I can tell you a bit about the aplications of linear algebra, that will probably be useful in electrical engineering.

1) Electrical circuits
The use of Kirchoff's laws will give you a system of linear equations, which is best solved for complicated systems by the use of linear algebra.

2) Applications of Electromagnetism
As vector calculus underlies electromagnetism, and classical electromagnetism is formulated in terms of vectors, linear algebra will be essential for more complicated problems. In particular you will be able to consider a change of coordite system, e.g. a rotated magnetic field.

Applications often involve infinite-dimensional vector spaces, in particular Fourier series. Such spaces are studied in functional analysis, which can be thought of a combination of linear algebra and calculus. It allows us to consider modes of the electromagnetic field as fourier components. Also

3) Signal processing
Fourier decomposition is essential for signal processing. Harmonic analysis allows you to obtain information from the signals you receive, by decomposing them.

4) Control Theory
Linear algebra is needed because control theory is about dynamical systems, which will satisfy differential equations or difference equations. The tools from linear algebra will be important to study the behaviour of the systems as you adjust your input.

5) Computational Engineering & Numerical Methods
Linear algebra is of great importance here, because many algorithms are about solving systems of linear equations. In order to properly understand algorithms, and their range of validity (sometimes an algorithm will give nonsese results), linear algebra is necessary. You may for example wish to analyse output data, and you will need numerical methods for that.

3. Aug 3, 2016

### icesalmon

Good, this is a good start! Thank you