Note : right click image---->select \"open image in new tab\" ~Please show ALL w

Question

Note: right click image---->select "open image in new tab"

~Please show ALL work answer thoroughly with a step by step explanation leading to the final answer. Thank you!

Let W be a subspace of the real vector space V. We say that a linear operator P : V rightarrow V is a projection operator onto W if P(V) = W and P(w) = w for all w W. Prove: A linear operator P : V rightarrow V is a projection operator if and only if P P := p2 = p. [Hint: If P2 = P, write every vector v V as v = P(v) + (v - P(v)). Conclude that V = Vo(P) + V1(P) and P is a projection operator onto V1(P).]

Explanation / Answer

I have written the answer and uploaded it as 2 pictures at the following links:

Part-1: http://i.imgur.com/SuHPeQ8.jpg

Part-2: http://i.imgur.com/VXqB3bN.jpg

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.