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math.RA2021
Towards a Singular Value Decomposition and spectral theory for all rings
Ran Gutin
We propose definitions of SVD, spectral decomposition (for self-adjoint matrices) and Jordan decomposition which make sense for all rings. For many rings, these decompositions can…
math.RA2021
An analogue of the relationship between SVD and pseudoinverse over double-complex matrices
Ran Gutin
We present a generalisation of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be…
math.RA2021
Matrix decompositions over the double numbers
Ran Gutin
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers.…