Advanced Form
For a vector space V and subspace W, a shear fixing W translates all vectors parallel to W.
To be more precise, if V is the direct sum of W and W′, and we write vectors as
- v = w + w′
correspondingly, the typical shear fixing W is L where
- L(v) = (w + Mw′) + w ′
where M is a linear mapping from W′ into W. Therefore in block matrix terms L can be represented as
with blocks on the diagonal I (identity matrix), with M above the diagonal, and 0 below.
Read more about this topic: Shear Mapping
Famous quotes containing the words advanced and/or form:
“But generally speaking philistinism presupposes a certain advanced state of civilization where throughout the ages certain traditions have accumulated in a heap and have started to stink.”
—Vladimir Nabokov (1899–1977)
“But labor of the hands, even when pursued to the verge of drudgery, is perhaps never the worst form of idleness. It has a constant and imperishable moral, and to the scholar it yields a classic result.”
—Henry David Thoreau (1817–1862)