How to Show that PL is a Matrix in Vector Projection?

[John Smith]

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

 

[HallsofIvy]

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.