# \(\text{Equilibrate}\)¶

You can use the \(\text{Equilibrate}\) to calculate scale factors to apply to a matrix that will minimize the condition number of a matrix. The function rescale row and column values to minimize the condition number of a matrix. The function will rescale row and column values such that the largest absolute value of any value in a row and column is 1.

You can use the `\equilibrate`

backslash command to insert this function.

The following variants of this function are available:

\(\text{tuple } \text{Equilibrate} \left ( \text{<matrix>} \right )\)

The \(\text{Equilibrate}\) function returns a tuple containing:

A diagonal matrix containing the row scale factors to be applied to reduce the condition number.

A diagnonal matrix containing the column scale factors to be applied to reduce the condition number.

A boolean value holding

`true`

if the operation was successful.

You can calculate the rescaled or equilibrated matrix by simply multiplying the incoming \(\text{<matrix>}\) by the calculated row and column matricies.

Figure 126 shows the basic use of the \(\text{Equilibrate}\) function.