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The process of balancing a matrix applies similarity transformations
to make the rows and columns have comparable norms. This is
useful, for example, to reduce roundoff errors in the solution
of eigenvalue problems. Balancing a matrix *A* consists
of replacing *A* with a similar matrix

A' = D^(-1) A D

where *D* is a diagonal matrix whose entries are powers
of the floating point radix.

- Function:
*int***gsl_linalg_balance_matrix***(gsl_matrix **`A`, gsl_vector *`D`) This function replaces the matrix

`A`with its balanced counterpart and stores the diagonal elements of the similarity transformation into the vector`D`.