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Almost every unit matrix is a \(ULU\). (English) Zbl 0893.15004
The author shows that almost every matrix of unit determinant can be written as \(ULV\), where all three factors have unit spectrum and, moreover, \(U\) and \(V\) are upper triangular while \(L\) is lower triangular.

15A23 Factorization of matrices
15B57 Hermitian, skew-Hermitian, and related matrices
Full Text: DOI
[1] David Kazhdan, Personal communication, 1995.
[2] Margolus, Normal; Toffoli, Tommaso, Cellular automata machines, (), 219-248 · Zbl 0655.68055
[3] Paeth, Alan, A fast algorithm for general raster rotation, (), 179-195, reprinted with corrections and additions
[4] Gilbert Strang, Every unit matrix is a LULU, Linear Algebra Appl., to appear. · Zbl 0918.15004
[5] Thévenaz, Philippe; Unser, Michael, Efficient geometric transformations and 3-D image registration, (), 2919-2922
[6] Tommaso Toffoli and Jason Quick, Three-dimensional rotations by three shears, Graphical Models and Image Processing, to appear.
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