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# 代写数学课业 Dual Space代写

2022-05-05 15:31 星期四 所属： 数学代写 浏览：61

## HW4 – Dual Space, Determinant, Rotations

### Remarks:  代写数学课业

A) Definition is just a definition, there is no need to justify or explain it.

B) Answers to questions with proofs should be written in the followingformat:

i) Statement and/or Result.

ii) Main points that will appear in your proof.

iii) The actual proof.

C) Answers to questions with computations should be written in thefollowing format:

i) Statement and/or Result.

ii) Main points that will appear in your computation.

iii) The actual computation.

### 1.  代写数学课业

Dual space. Let V be a finite dimensional vector space over a field F.

The dual space of V , denote V* , is defined to be the space

V* = Hom(V, F) = {φ : V → F; φ is linear transformationg},

of all linear transformations from V to F. The elements of V* are, sometime, called functionals.

(a) Show that dim(V ) = dim(V* ).

(b) Suppose now that F = R, and V is an inner product space, with inner product ( , ). Consider the natural mapping

### 3.  代写数学课业

The orthogonal group O2. We know that

O2 ={A ∊GL2; AAt = I2}:            (2)

• You are welcome to consult the lecturer on HW during office hours.
• You are very much encouraged to work with other students on the HW.
• You should submit your HW ALONE in YOUR OWN ORIGINAL DOCUMENT!!!

Good Luck!