You can use the \(\text{LQ}\) function to perform an LQ decomposition of a real or complex matrix, creating the \(L\) lower triangular matrix and a \(Q\) unitary matrix.

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

The following variants of this function are available:

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

The \(\text{<matrix>}\) is a real or complex matrix. Boolean and integer matrices are automatically upcast to real matrices.

The function returns a tuple containing:

  • The \(L\) lower triagular matrix.

  • The \(Q\) unitary matrix.

  • A boolean flag indicating success (true) or (false).

Figure 175 shows the basic use of the \(\text{LQ}\) function.


Figure 175 Example Use Of The LQ Function