What would you like to understand?

Minimizing the Euclidean norm $\|\vec{b} - A\vec{x}^*\|$ is equivalent to minimizing its square, $\|\vec{b} - A\vec{x}^*\|^2$. The squared norm expands algebraically into the sum of the squared differences of corresponding components: $(b_1 - v_1)^2 + (b_2 - v_2)^2 + \cdots + (b_n - v_n)^2$, where $\vec{v} = A\vec{x}^*$.

Conditions: $\vec{b}, \vec{v} \in \mathbb{R}^n$; Standard Euclidean norm is used; $\vec{v} = A\vec{x}^*$

Minimizing the Euclidean norm $\|\vec{b} - A\vec{x}^*\|$ is equivalent to minimizing its square, $\|\vec{b} - A\vec{x}^*\|^2$. The squared norm expands algebraically into the sum of the squared differences of corresponding components: $(b_1 - v_1)^2 + (b_2 - v_2)^2 + \cdots + (b_n - v_n)^2$, where $\vec{v} = A\vec{x}^*$.

Conditions: $\vec{b}, \vec{v} \in \mathbb{R}^n$; Standard Euclidean norm is used; $\vec{v} = A\vec{x}^*$