Thread: Hyperplane

Dear Colleagues,

Could you please help me in solving the following problem:
If is a subspace of a vector space and codim , then every element of is called a hyperplane parallel to . Show that for any linear functional on , the set is a hyperplane parallel to the null space of .


Regards,

Raed.

Originally Posted by raed

Dear Colleagues,

Could you please help me in solving the following problem:
If is a subspace of a vector space and codim , then every element of is called a hyperplane parallel to . Show that for any linear functional on , the set is a hyperplane parallel to the null space of .


Regards,

Raed.

Hints:

S\Definition: A subspace of a vector space is called a hyperplane iff it is a maximal

subspace of it, i.e.

Claim: a subspace of a vec. sp. is a hyperplane iff it is the kernel of a non-zero linear

functional on the space

Claim: a subspace of a finite dimensional v.s. is a hyperplane iff its dimension is one less

that then space's.

Tonio