Linear Algebra I - A collection of exercises and solution aimed for the first semester.

Linear Algebra II
- A collection of exercises and solution aimed for the course Linear Algebra II.

Here is a phone version.

Linear Algebra for teachers
- A collection of exercises and solution plus some short notes on theory.

Here is a phone version.

Email: per.w.alexandersson@gmail.com.

#About me
I recently started as a postdoc at KTH, Stockholm, working with Svante Linusson.
Before that, (2015-2017) I worked as a postdoc at University of Pennsylvania,
with Jim Haglund, funded by a grant from the Knut and Alice Wallenberg foundation.
In 2014, I worked as a postdoc at Universität Zurich, Schweiz with Valentin Féray.
My field of research is representation theory and combinatorics, more specifically,
polynomials given by structure constants (Kostka-coefficients, characters of the symmetric group)
and Jack generalizations of these, as well as chromatic symmetric functions, LLT polynomials and so on.
In Spring 2013 I defended my thesis titled _Combinatorial Methods in Complex Analysis_,
where Boris Shapiro was my primary advisor. My research interests are mainly combinatorics,
complex analysis and algebraic geometry.
My favorite research tools are _Mathematica_, _OEIS_, _FinstStat_, _MathOverflow_, _WolframAlpha_ and _Google_.
I am also a bit interested in special polynomials,
for example real-rooted polynomials, and polynomials obtained from
combinatorial statistics.
Finally, I must admit that I have a soft spot for tilings, discrete dynamical systems,
machine learning, neural networks and cellular automata.
##List of publications
* *(W. Mehtaab Sawhney) Properties of non-symmetric Macdonald polynomials at $q=0$ and $q=1$*, (arxiv)
* *(W. Greta Panova) LLT polynomials, chromatic quasisymmetric functions and graphs with cycles*, (submitted) (arxiv)
* *(W. Mehtaab Sawhney) A major-index preserving map on fillings*, Electronic Journal of Combinatorics **24**, No.4 (2017)
* *Polytopes and large counterexamples*, Experimental Mathematics, (2017) 1–6
* *Non-symmetric Macdonald polynomials and Demazure-Lusztig operators*, (submitted), (arxiv)
* (With. V. Féray) *Shifted symmetric functions and multirectangular coordinates of Young diagrams*, Journal of Algebra **483** (2017), 262–305
* *Polynomials defined by tableaux and linear recurrences*, Electronic Journal of Combinatorics **23**, No.1 (2016)
* *Gelfand–Tsetlin polytopes and the integer decomposition property*, European Journal of Combinatorics, **54**, (2016)
* *A combinatorial proof the skew K-saturation theorem*, Discrete Mathematics (2015), 93–102
* (With B. Shapiro) *Around Mutlivariate Schmidt-Spitzer Theorem*, Linear Algebra and its Applications **446** (2014), 356–368
* *Stretched skew Schur polynomials are recurrent*, Journal of Combinatorial Theory, Series A **122** (2014) 1–8.
* *Schur polynomials, banded Toeplitz matrices and Widom's formula*, Electronic Journal of Combinatorics **19**, No.4 (2012)
* (With B. Shapiro) *Discriminants, symmetrized graph monomials, and sums of squares*, Experimental Mathematics **21** No. 4 (2012) 353–361
* *On eigenvalues of the Schrödinger operator with an even complex-valued polynomial potential*, CMFT **12** No.2 (2012) 465–481
* (With A. Gabrielov) *On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential*, CMFT **12** No.1 (2012) 119–144
##Other projects
In my spare time, I tinker a bit with a flame fractal renderer written in Java.
You can browse the source on Sourceforge.
On this website, you will also find several of my smaller projects.
They revolve around
*Mathematica*, *LaTeX*, *Programming*, *Generative art* and other things related to mathematics.
##About this website
I use MathJax for rendering mathematics and a Markdown converter for the contents.