\(\text{Rank}\)

You can use the \(\text{Rank}\) function to determine the rank of a matrix.

You can use the \rank backslash command to insert this function.

The following variants of this function are available:

• \(\text{integer } \text{Rank} \left ( \text{<matrix>}, \text{<tolerance>} \right )\)

The \(\text{<matrix>}\) parameter is the matrix to determine the rank of. The \(\text{<tolerance>}\) is a scalar tolerance to apply to the matrix rank calculation.

The \(\text{Rank}\) function returns an integer value indicating the rank of the matrix.

The function calculates the matrix rank using singular value decomposition producing a square diagonal matrix \(\Sigma\) and two semi-unitary matrices. The matrix rank is then determined by counting the number of diagonal entries in \(\Sigma\) whose magnitude is greater than the provided tolerance.

Figure 191 shows the basic use of the \(\text{Rank}\) function.

Figure 191 Example Use Of The Rank Function