Does there exist a linear map from the set of 24x29 Matrices to the set of Symmetric Positive definite (SPD) 24x24 Matrices? I understand that matrix multiplication is a linear map but from the matrix to the SPD form, is there some sort of a linear map? Prove or disprove.
2026-03-29 20:23:44.1774815824
Existence of a linear map to the space of SPD matrices
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The codomain does not contain a zero element, so any linear map is undefined at the $24\times29$ zero matrix. No such linear map can exist. More generally, it doesn't make sense to define a linear map to a set that is not closed under vector operations.