- #1
Emspak
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pproving (g ° f)* = f* ° g* -- is this correct?
assume g: F→G is a linear map
prove that (g ° f)* = f* ° g*
My solution
(g ° f)* = g* ° f* by the properties of associativity in linear maps.
if we assume that g* ° f* = f* ° g* then g and f are inverse functions of each other.
by the properties of linear maps the only way that g* ° f* = f* ° g* is if they are inverse functions.
therefore (g ° f)* = f* ° g*
is there anything wildly wrong with my reasoning?
Homework Statement
assume g: F→G is a linear map
prove that (g ° f)* = f* ° g*
My solution
(g ° f)* = g* ° f* by the properties of associativity in linear maps.
if we assume that g* ° f* = f* ° g* then g and f are inverse functions of each other.
by the properties of linear maps the only way that g* ° f* = f* ° g* is if they are inverse functions.
therefore (g ° f)* = f* ° g*
is there anything wildly wrong with my reasoning?