# $$\text{Equilibrate}$$¶

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.

Figure 126 Example Use Of The Equilibrate Function