Abstract
The four matrices L 0 U 0 L 1 U 1 at the end of the title are triangular with ones on their main diagonals. Their product has determinant one. Following a question and theorem of Toffoli, we show that any matrix with determinant one can be factored in this way. A transformation of the plane becomes a sequence of one-dimensional shears, with n 2 — 1 free parameters.
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