### 14.19 Balancing

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.