Matrix Square Root Calculator

About this calculator

The square root of a matrix A is a matrix B such that B² = A — a natural extension of ordinary square roots into linear algebra, but one that isn't always unique or guaranteed to exist for every matrix. For a general 2×2 matrix, the principal square root can be computed directly from a closed-form formula involving the matrix's trace (the sum of its diagonal entries) and determinant, without resorting to eigendecomposition.

This calculator takes the four entries of a 2×2 matrix and returns its principal square root along with its trace and determinant. Matrix square roots show up in control theory, computer graphics (interpolating rotation and transformation matrices), and numerical methods for solving matrix equations, making this a useful reference for students and practitioners who need to verify a hand calculation or quickly check a specific 2×2 case.