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Visualisation of polar decomposition of linear transformations

Erik Hrvatin (2017) Visualisation of polar decomposition of linear transformations. Diploma thesis.

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    Abstract

    The thesis aims at addressing the polar decomposition of a real square matrix. This is the product of a positive-definite matrix and an orthogonal matrix that are discussed in more detail as well. It is shown and proved in the thesis that the polar decomposition always exists and it is unique for invertible matrices. The adequate formula for orthogonal and positive-definite 2x2 matrices and the explicit formula for the polar decomposition of 2x2 matrices are derived. The latter can be used to help us determine when a polar decomposition of a matrix has rational coefficients. Matrices can also be seen as linear transformations of the plane. They can be visually represented with images or interactive applets that were developed using the GeoGebra program.

    Item Type: Thesis (Diploma thesis)
    Keywords: matrix, positive-definite matrix, orthogonal matrix, polar decomposition, linear transformation, visualisation
    Number of Pages: 42
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    doc. dr. Boštjan KuzmanMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11695433)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4654
    Date Deposited: 13 Sep 2017 09:16
    Last Modified: 13 Sep 2017 09:16
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4654

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