What is arbitrary matrix?

An arbitrary matrix is a matrix whose elements are not specified or constrained, allowing for any values to be assigned. It is often represented using variables (e.g., ( A = \begin{pmatrix} a_{11} & a_{12} \ a_{21} & a_{22} \end{pmatrix} )), where the elements can take on any real or complex numbers. Arbitrary matrices are commonly used in mathematical proofs and theoretical discussions to illustrate concepts without being tied to specific numerical examples.