Codimension of the null space

Dear Colleagues,

Could you please help me in the following problem:

Let be any linear functional on a vector space show that in the quotient space the codim . Here denotes the null space of , and codim means the dimension of .

Remark: two elements belong to the same element of the quotient space if and only if .


Regards,

Raed.

Hint :


If then, i.e. .

I do not understand.

Quote:

---

Originally Posted by raed

I do not understand.

---

What does mean is different from ?

Quote:

---

Originally Posted by raed

I do not understand.

---

Please be more specific. What part do you not understand?

Do you understand what a linear functional is?

(I puzzled over FernandoRevilla's response until I realized I had read "functional" but was still thinking "transformation"!)