Postby Technomancer » Sun Sep 21, 2003 5:15 am
The Singular Value Decomposition is a common matrix operation, often used in least-squares problems. It can be thought of as being similar to an eigendecomposition.
For the SVD, given a real NxM matrix X of rank r, it can be decomposed as:
X=USV(H) (H) indicates the conjugate transpose ie. Hermitian operator
U is an NxN unitary matrix
V is an MxM unitary matrix
S is an NxM diagonal matrix, with r elements called singular values.
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov