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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.

##### MSC:
 15A23 Factorization of matrices 15B57 Hermitian, skew-Hermitian, and related matrices
##### Keywords:
unit matrix; triangular matrix; matrix factorization
Full Text:
##### References:
 [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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