Hi,
I didn't succeed in solving these two short questions.
1. Let it be V inner product space of finite dimensional.
Let it be W, U sub spaces of V. prove:
. . .\(\displaystyle \left(W^{\perp}\, +\, U^{\perp}\right)\, \geq\, \left(W\, \bigcap\, U\right)^{\perp}\)
2. Let it be V inner product space of finite dimensional.
Let it be \(\displaystyle \, T\, :\, V\, \rightarrow\, V\, \) linear operator. prove:
. . .\(\displaystyle \mbox{Im } T^*\, \geq\, \left(\mbox{Ker } T\right)^{\perp}\)
in the first one I think I need to work with bases, but I don't know how.
In the second question I just don't know how to start.
Can you show me how to solve these?
I didn't succeed in solving these two short questions.
1. Let it be V inner product space of finite dimensional.
Let it be W, U sub spaces of V. prove:
. . .\(\displaystyle \left(W^{\perp}\, +\, U^{\perp}\right)\, \geq\, \left(W\, \bigcap\, U\right)^{\perp}\)
2. Let it be V inner product space of finite dimensional.
Let it be \(\displaystyle \, T\, :\, V\, \rightarrow\, V\, \) linear operator. prove:
. . .\(\displaystyle \mbox{Im } T^*\, \geq\, \left(\mbox{Ker } T\right)^{\perp}\)
in the first one I think I need to work with bases, but I don't know how.
In the second question I just don't know how to start.
Can you show me how to solve these?
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