Least Squares Estimation - Problem with Symbols

[Schnurmann]

Hi folks,
1. Homework Statement
I don't fully understand the question statement, how is it supposed to be read?
Question:
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∈ℝ^m×n and b∈ℝ^m are given. You can assume that A has rank n. Justify your answer.

Homework Equations

How do i read the part where set symbols are mentioned?

 

[Schnurmann]

Okay i have another question:
How do we find the minimizer of a norm function?

 

[Mark44]

Hi folks,
1. Homework Statement
I don't fully understand the question statement, how is it supposed to be read?
Question:
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∈ℝ^m×n and b∈ℝ^m are given. You can assume that A has rank n. Justify your answer.

Homework Equations

How do i read the part where set symbols are mentioned?

A is an m x n matrix, and b is an m-dimensional vector.

Okay i have another question:
How do we find the minimizer of a norm function?

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.