Geodesic
On semi-orthogonal matrices with row vectors of equal lengths
Kalle Leppälä1
1University of Helsinki, The Organismal and Evolutionary Biology Research Programme
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 621–629

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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.
DOI : 10.54330/afm.152122
Keywords: Orthogonal, semi-orthogonal, Grassmann coordinates, isometric perspective, axonometry

Kalle Leppälä  1

1 University of Helsinki, The Organismal and Evolutionary Biology Research Programme 
Kalle Leppälä. On semi-orthogonal matrices with row vectors of equal lengths. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 621–629. doi: 10.54330/afm.152122
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