A note on homotopies of rational matrix inner functions

Key Points

• The aim is to show the path connectedness of the space of rational inner functions in a specific matrix context.
• Analyzed the conditions under which the space of rational matrix functions remains connected.
• Applied mathematical theories related to homotopies and inner functions.
• Considered matrix dimensions where m is greater than n.
• Demonstrated that the space of rational matrix inner functions is path connected when m > n.
• Established an important link between matrix function properties and connectedness in mathematical analysis.