Sqrt - Square Roots of Matrices and Operators

Square Roots of Matrices and Operators

If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we then define A1/2 = √A = B. In general matrices may have multiple square roots or even an infinitude of them. For example the 2×2 identity matrix has an infinity of square roots.