# Correct notation for taking the element-wise square root of a matrix

As the title says, I'm pretty confused how I can, in correct mathematical notation, note that the square root of each element of a matrix needs to be taken. If

$$A \triangleq \left[ \begin{array}\\ x_1, x_2 \\ x_3, x_4 \end{array} \right]$$

what is the correct notation for $$\sqrt{A}$$ where $$\sqrt{A} \triangleq \left[ \begin{array}\\ \sqrt{x_1}, \sqrt{x_2} \\ \sqrt{x_3}, \sqrt{x_4} \end{array} \right] ?$$

Essentially, what is the correct symbol I attach to $$A$$ to indicate element-wise square roots are to be taken?

• Different contexts will use different notation for this idea. Sometimes, the notation $A^{\circ 1/2}$ is used. Aug 12 '20 at 21:12
• Great! Also good to know what I'm referring to is the Hadamard root. If you post this as an answer, I'll accept it. Aug 12 '20 at 21:19

Sometimes this is referred to as the Hadamard root and is referred to with notation $$A^{\circ 1/2}$$.