In lecture 15 (The first five minutes), the professor explains how the orthogonality law is derived. He shows how to find the length of the orthogonal line from b to a.

However, what I don't understand is that the professor says these are one dimensional while I think two lines in a plane are one dimensional .
Can you please explain this to me ?

Question

In lecture 15 (The first five minutes), the professor explains how the orthogonality law is derived. He shows how to find the length of the orthogonal line from b to a.

However, what I don't understand is that the professor says these are one dimensional while I think two lines in a plane are one dimensional .
Can you please explain this to me ?

joshdanziger23 · Answer

Salehmamdouh1984, when Prof Strang refers to there being one dimension he's referring to the space he wants to project onto, ie, all vectors making up the line a. The system he draws on the board is clearly two-dimensional and all his vectors (including a) are in R2; but vectors along the line a make up a one-dimensional subspace within R2. b is outside this subspace and the question Prof Strang wants to answer is to which vector within the subspace is "closest" to b.