The discussion focuses on demonstrating that the projection operator PL is represented as a matrix in vector projection. The matrix representation of PL, given a direction vector d = [a, b, c], is defined as 1/(a² + b² + c²) multiplied by the matrix:
[a² ab ac; ab b² bc; ac bc c²]. It is clarified that PL is a linear transformation, and the matrix representation is straightforward when the basis aligns with the direction vector components. The participants express confusion regarding the notation used to represent the matrix.
Mathematicians, physics students, computer graphics developers, and anyone interested in linear algebra and its applications in vector projections and transformations.
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 ...!John Smith said: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