Show that PL has matrix

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Main Question or Discussion Point

Let PL an QL denote, respectively, projection on and reflection in the line L through the origin with direction vector d = [a b c] =not 0

I got a proplem showing that PL is a matrix.

1/(a^2 +b^2+c^) = Matrix......a^2 ab ac
..........................................ab b^2 bc
..........................................ac bc c^2
 

Answers and Replies

HallsofIvy
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Let PL an QL denote, respectively, projection on and reflection in the line L through the origin with direction vector d = [a b c] =not 0

I got a proplem showing that PL is a matrix.

1/(a^2 +b^2+c^) = Matrix......a^2 ab ac
..........................................ab b^2 bc
..........................................ac bc c^2
Strictly speaking, PL is a linear transformation. You are talking about it's matrix representation in the basis in which the given line has direction vector with components [a b c]. Now, unfortunately, I have no idea what you mean by "1/(a^2+ b^2+ c^2)= Matrix ...!

Given a vector [x y z], how would you find its projection, PL[x y z]? I get that the matrix representation is a very simple diagonal matrix.
 

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