Affine transformations of the plane and their geometrical properties

TL;DR

This paper explores how polar decomposition helps understand the metric properties of affine transformations in the plane, providing insights suitable for students with linear algebra background.

Contribution

It introduces a geometric perspective on affine transformations using polar decomposition, emphasizing their metric properties in two-dimensional space.

Findings

Polar decomposition clarifies the metric effects of affine transformations.

The approach aids in visualizing linear operators' geometric properties.

Educational insights for students with linear algebra knowledge.

Abstract

In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non-degenerate linear operators in $R^2$.