Matrix square roots are related to square roots of real numbers: say that the matrix B is a square root of the matrix A if B*B = A. If A is positive semidefinit

Matrix square roots are related to square roots of real numbers: say that the matrix B is a square root of the matrix A if B*B = A. If A is positive semidefinite, then it admits a unique positive semidefinite square root in the same way that a positive real number admits a positive real square root. So I would say that the notion of matrix square roots is as obviously related to the notion of real square roots as possible.