On semi-orthogonal matrices with row vectors of equal lengths
Year: 2024
Type: article
Abstract: When does a rectangular matrix with an orthonormal set of column vectors have row vectors of equal lengths? The column spaces of such matrices are multidimensional generalizations of the projection plane used in isometric perspective. We show that in the absence of unexpected linear relations, any rectangular matrix can be row-scaled so that if we were to orthonormalize the column vectors, the row vectors would attain equal lengths in the process. We use Grassmann coordinates to reduce the question into an instance of the famous matrix scaling problem, and with the help of existing theory introduce simple numerical solutions.
Source: Annales Fennici Mathematici
DOI: 10.54330/afm.152122
Author: Kalle Leppälä
Institution: University of Helsinki
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404331420