feat(linear_algebra/matrix): linear maps are linearly equivalent to matrices #1310
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added 7 commits
August 9, 2019 11:22
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This looks nice to me! But I'll wait for others using the linear algebra library to chime in before approving. @ChrisHughes24 , any thoughts?
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Someone needs to fry up some exterior powers |
ChrisHughes24
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Aug 16, 2019
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…atrices (leanprover-community#1310) * linear map to matrix (WIP) * WIP * feat (linear_algebra/matrix): lin_equiv_matrix * feat (linear_algebra.basic): linear_equiv.arrow_congr, std_basis_eq_single * change unnecessary vector_space assumption for equiv_fun_basis to module * add docstrings and refactor * add docstrings * move instance to pi_instances * add docstrings + name change * remove duplicate instance
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In addition to the already existing to_lin function which sends a matrix to its corresponding linear map, I defined a to_matrix function which sends a linear map to its corresponding matrix (using the standard basis for
n → α). Given bases for general vector spacesβandγoverα, we get a linear equivalence between linear mapsβ →l[α] γand matrices overαindexed by these bases.I wanted this equivalence to define the determinant of a linear map. Although we may not need it for that reason in the future, it seems useful to have nevertheless.