User:IssaRice/Linear algebra/Properties preserved under various operations to a matrix

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Revision as of 05:42, 17 January 2020 by IssaRice (talk | contribs) (Created page with "properties to discuss: {| class="sortable wikitable" |- ! Operation !! Preserved properties !! Properties not necessarily perserved |- | Elementary operation: swapping rows...")
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properties to discuss:

Operation Preserved properties Properties not necessarily perserved
Elementary operation: swapping rows
Elementary operation: shear
Elementary operation: scaling one row
Transpose
Inverse
Formation of adjoint (conjugate transpose)
Multiplication by an invertible matrix
Multiplication by an elementary matrix
Change of basis (A↦QAQ−1 for some invertible Q)

inspired by questions 5 and 6 at http://scherk.pbworks.com/w/page/14864231/Quiz%3A%20Linear%20algebra

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