# $$\text{LQ}$$¶

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