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‘A Generalisation of the Determinant to Rectangular Matrices: Implications in Gauge Theory’

Abhimanyu Sudhir - Class 9 C :
In this paper, I proposed a generalisation of the determinant to rectangular matrices and demonstrate its relation to the previously-known vector determinant. I then proceeded to find a few properties of this new determinant-like function. Finally, the implications of the determinant-like function in gauge theory are discussed, as the determinant-like function and rectangular groups form the motivation to study non-square metric tensors in gauge theory. The dimensions of various tensors on a manifold with a 4 by 3 metric are found. It is seen that the shear stress and the momentum behave in an exotic manner on such a manifold.