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The
Geometry of Collinearity - 1
z1
z2
Basis vectors
r2
r1
z=Data value
= 1.3×r1+1.1×r2
Non-collinear
(well-posed)
z1
z2
r2
r1
z=Data value
= -1.8×r1+7.2×r2
Near-collinear
(ill-posed)
¥ Trying to fit data as a sum of basis vectors that are nearly parallel doesnÕt work well: solutions can
be huge
¥ Exactly parallel basis vectors would be impossible:
¥ Determinant of matrix to invert would be zero