The Approximation of One Matrix by Another of Lower Rank

  title={The Approximation of One Matrix by Another of Lower Rank},
  author={Carl Eckart and G. Young},
The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written do~vn, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matrices in a canonic form. It is found that the problem always has a solution which is usually unique… CONTINUE READING
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