Further characterizations and representations of the Bott-Duffin core inverse

Key Points

• The aim is to discuss new characterizations and representations of the Bott-Duffin core inverse.
• Characterized the Bott-Duffin core inverse using orthogonal projectors and matrix equations.
• Presented representations through full-rank decomposition.
• Provided least-squares solutions for constrained linear equations.
• New characterizations were established using orthogonal projectors and the Bott-Duffin group inverse.
• Representations of the Bott-Duffin core inverse are effectively illustrated through full-rank decomposition.
• The least-squares solution for constrained systems of linear equations was derived.