Furthermore, we show that every transformation induced by a general parquet matrix has a factor in this special class.
This is no longer true for general parquet maps.
For this class of parquet matrices we get the following.
However, there is a class of parquet matrices whose inverses are parquet, and these inverses induce the inverse transformations.
However, there is a special class of parquet matrices where the inverse of the matrix induces the inverse transformation.
Notice in the above definition that the parquet property is a relative one that depends on a particular fundamental set.
Moneo's interiors, on the contrary, have a characteristic of finality: the floors are of patterned parquet on which it is hard to put anything diagonal or non-orthogonal.
These two statements can be used to give an algorithm for determining when an (n x n) matrix is parquet, which we leave as an exercise.
