How do I solve for H in matlab?

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SUMMARY

The discussion focuses on solving for the unknown matrix H in MATLAB, given the relationship Z = HTH, where Z is defined as Z = A + 2*eye(n). The matrix A is known, and it is established that both Z and A must be symmetric and positive definite. The Cholesky decomposition function in MATLAB, specifically chol, is recommended for obtaining the matrix H, which will be lower triangular.

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  • Understanding of matrix algebra, specifically properties of symmetric and positive definite matrices.
  • Familiarity with MATLAB programming and syntax.
  • Knowledge of Cholesky decomposition and its applications in solving matrix equations.
  • Basic concepts of eigenvalues and eigenvectors related to matrix properties.
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This discussion is beneficial for MATLAB users, data scientists, and engineers who are working with matrix equations, particularly those needing to implement matrix decompositions for solving linear systems.

Badger33
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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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