Linear Algebra & Mapping Diagrams: Old & New Visualizations
- Author:
- Martin Flashman
https://www.geogebra.org/m/vydftwmb
Linear Algebra and Mapping Diagrams: Old & New Visualizations
Visualizing Linear (Matrix) Transformation Algebra is explored with mapping diagrams for maps from .
The visualization of 2 x 2 matrix (linear) transformations
traditionally has been created as a geometric transformation of planar
figures in a cartesian plane or as a mapping diagram between two
frames representing distinct cartesian planes. In this presentation
Professor Flashman will review core concepts of linear algebra with
these visualizations while introducing a new visualization created
using GeoGebra of mapping diagrams between parallel cartesian planes
in 3 dimensions. Of special interest are visualizations of matrix
multiplication as composition and Gauss Jordan Elimination in solving
linear equations and finding inverses.
GeoGebra activities will be available on-line. Some familiarity with
elementary matrix algebra will be presumed.
Table of Contents
Introduction: Motivation
R^2 and Other Vector Spaces
Matrix Linear Transformations on R^2
- Linear MD: R^2 to R
- 2x2 Matrix Transformation Traditional Views
- Introducing 2x2 Matrix Transformation Mapping Diagrams
- Matrix Transformation on Circle
- Matrix Multiplication/Composition
- Eigenvectors and Mapping Diagrams I
- Eigenvectors and Mapping Diagrams II
- Matrix Transformations on R^3: Mapping Diagrams. Eigen-vectors/values.
Solving Linear (Matrix) Equations
Markov Chains