Then, by the definition of the hat matrix, which is the projection matrix onto the column space of X, that is, Note that H is an n × n matrix. then, By the commutative property of the trace ...
When P projects onto the column space of A, I P projects onto the . Solution (4 points) (I 2P) = I 2 2IP PI + P = I 2P + P = I 2P + P = I P: 5
discarded. As a result, the column space of + spans a lin-ear sub-space that best represents the statistical variability of the data. The projection matrix +4+51 projects any target image (spread as a vector 6) onto the linear subspace: 7 6 8+4+ 1. The columns of + are called the Principle Components of the ensemble, and in the context of Vision general, projection matrices have the properties: PT = P and P2 = P. Why project? As we know, the equation Ax = b may have no solution. The vector Ax is always in the column space of A, and b is unlikely to be in the column space. So, we project b onto a vector p in the column space of A and solve Axˆ = p. Projection in higher dimensions
Updated on June 30 Sat, 04:04 PM, 2018
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