SQRTM

Purpose:

Computes the principal matrix square root.

SQRTM(a)

(x, res) = SQRTM(a)

A square matrix.

A square matrix.

(x, res) = SQRTM(a) returns the square root matrix and residual where res = norm(a - x *^ x, "fro") / norm(a, "fro").

W1: ravel(1..9, 3)

W2: sqrtm(W1)

W3: real(W2 *^ W2)

W1 contains the array:

{{1, 4, 7},

{2, 5, 8},

{3, 6, 9}}

W2 == {{0.4498 + 0.7623i, 1.0185 + 0.0842i, 1.5873 - 0.5940i},

{0.5526 + 0.2068i, 1.2515 + 0.0229i, 1.9503 - 0.1611i},

{0.6555 - 0.3487i, 1.4844 - 0.0385i, 2.3134 + 0.2717i}}

W3 == {{1, 4, 7},

{2, 5, 8},

{3, 6, 9}}

SQRTM(A) returns a matrix X such that X *^ X == A.

Not all matrices have a square root and some matrices have multiple square roots.