Square Root

Tensorial (matrix) square root of a positive definite rank 2 Tensor. For algorithmic details see Franka, L.P. (1988). This function can be used to obtain the stretch tensor. For a rank 1 Tensor (vector), the element-wise square root is returned.

\[\begin{align} \mathbf{C} &= \mathbf{U}^2 \\ \mathbf{U} &= \sqrt{\mathbf{C}} \end{align}\]

Property	Value
Result	Tensor-valued function
Data Types	Tensor2, Tensor2s

Example

type(Tensor2)  :: F, R

type(Tensor2)  :: U, C
! type(Tensor2s) :: U, C

C = transpose(F)*F
U = sqrt(C)

! polar decomposition F = R*U
R = F*inv(U)