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Diagonalization back in <acroref type="section" acro="SD" /> was really a change of basis to achieve a diagonal matrix repesentation. Maybe we should be highlighting the more general <acroref type="theorem" acro="MRCB" /> here, but its overly technical description just isn't as appealing. However, it will be important in some of the matrix decompostions in <acroref type="chapter" acro="MD" />.
+Diagonalization back in <acroref type="section" acro="SD" /> was really a change of basis to achieve a diagonal matrix repesentation. Maybe we should be highlighting the more general <acroref type="theorem" acro="MRCB" /> here, but its overly technical description just isn't as appealing. However, it will be important in some of the matrix decompositions you will encounter in a future course in linear algebra.
This theorem, with the companion definition, <acroref type="definition" acro="EELT" />, tells us that eigenvalues, and eigenvectors, are fundamentally a characteristic of linear transformations (not matrices). If you study matrix decompositions in <acroref type="chapter" acro="MD" /> you will come to appreciate that almost all of a matrix's secrets can be unlocked with knowledge of the eigenvalues and eigenvectors.
+This theorem, with the companion definition, <acroref type="definition" acro="EELT" />, tells us that eigenvalues, and eigenvectors, are fundamentally a characteristic of linear transformations (not matrices). If you study matrix decompositions in a future course in linear algebra you will come to appreciate that almost all of a matrix's secrets can be unlocked with knowledge of the eigenvalues and eigenvectors.