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Homework Help: Least Squares Estimation - Problem with Symbols

  1. Nov 2, 2014 #1
    Hi folks,
    1. The problem statement, all variables and given/known data

    I don't fully understand the question statement, how is it supposed to be read?
    Give a formula for the minimizer x* (to be read as x-star) of the function ƒ:ℝn → ℝ, x → ƒ(x) = ||Ax-b||22, where A∈ℝm×n and b∈ℝm are given. You can assume that A has rank n. Justify your answer.

    2. Relevant equations
    How do i read the part where set symbols are mentioned?
  2. jcsd
  3. Nov 2, 2014 #2
    Okay i have another question:
    How do we find the minimizer of a norm function?
  4. Nov 3, 2014 #3


    Staff: Mentor

    A is an m x n matrix, and b is an m-dimensional vector.
    f(x) is always nonnegative, with a minimum value of 0, which occurs when Ax = b. Your textbook ought to have a discussion of how to find x in this case.
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