The aim of this project is to do some basic numerical linear algebra, programming in MATLAB and LaTeX.

We first introduce

1. Vector norms
2. Matrix norms
3. Singular value decomposition

as the preliminaries.

Then we introduce the main theory of our project, the polar decomposition.

Furthermore, we introduce two numerical methods and combine them together

1. Newton iteration
2. Newton Schulz iteration

Finally we test our code using several test matrices.

LaTeX related files are all located at the document folder, and the MATLAB related files are located at the code folder.

• File proj_description.pdf is the description of this project.
• File ./document/proj_polar.pdf is the report for this project.
• File ./code/poldec.m is the MATLAB code for the polar decomposition.
• File ./code/polsqrt.m is the MATLAB code for computing matrix square root using the polar decomposition.

Notice that some of the figures are located at ./code/ rather than ./document/figs/, and this is due to the export_fig command (for export figures in MATLAB) saves the figure to the current directory which is ./code/.