Let φ : V → V {\displaystyle {}\varphi \colon V\rightarrow V} be a linear mapping on a K {\displaystyle {}K} -vector space V {\displaystyle {}V} . Let v 1 , … , v n {\displaystyle {}v_{1},\ldots ,v_{n}} be a basis of V {\displaystyle {}V} , such that φ {\displaystyle {}\varphi } is described, with respect to this basis, by an upper triangular matrix. Show that the linear subspaces
are φ {\displaystyle {}\varphi } -invariant for every i {\displaystyle {}i} .
be a
linear mapping
on a
-vector space
. Let 
be a
basis
of , such that 
is described, with respect to this basis, by an
upper triangular matrix.
Show that the
linear subspaces
-invariant
for every 
.
