How do I solve for H in matlab?

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To solve for the unknown matrix H in MATLAB given the relationship Z = HTH, the matrix Z must be symmetric and positive definite. The known matrix A is used to construct Z with the equation Z = A + 2*eye(n), where n is an integer. The Cholesky decomposition function, chol, in MATLAB can be utilized to compute H, as it returns a lower triangular matrix that satisfies the required properties. It's important to ensure that both A and Z meet the positive definiteness criteria. This approach effectively allows for the calculation of H based on the defined relationship.
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I need help implementing this bit of code into matlab. I have a known matrix lest call it Z. and I have another unknown matrix called H. The matrices are related by the following relationship.

Z = HTH

How do I solve for H in matlab? If it is relevant Z is a make up of other known matrices and that code in MATLAB is:

Z = A + 2*eye(n)

where A is the initial known matrix and n is just an integer.UPDATE: Yes A and Z will always be positive.
 
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As an initial observation Z has to be symmetric and positive definite to do this, which puts restrictions on A. Assuming that this is true,

http://www.mathworks.com/help/matlab/ref/chol.html

is what you're looking for. This returns a matrix H that has the property you want and also is lower diagonal
 
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see update
 

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