Abstract
We prove an integral representation and a power series expansion for the function \(\det (A)^{-1}\) in a small neighborhood of the identity matrix. Both results are closely linked to the formula for the change of coordinates of the Dirac delta distribution in 
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A. Guzmán Adán is supported by a postdoctoral fellowship of the Research Foundation—Flanders (FWO)
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Acknowledgements
The authors want to thank Dr. Michael Wutzig for the careful reading of the manuscript and his valuable suggestions. Alí Guzmán Adán is supported by a postdoctoral fellowship of the F.W.O. Research Foundation-Flanders Belgium (180791/1262021N).
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Constales, D., Guzmán Adán, A. (2021). Representation Formulae for the Determinant in a Neighborhood of the Identity. In: Alpay, D., Peretz, R., Shoikhet, D., Vajiac, M.B. (eds) New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative. Operator Theory: Advances and Applications(), vol 286. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-76473-9_8
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DOI: https://doi.org/10.1007/978-3-030-76473-9_8
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