Two Methods to Find Standard Matrix for Projection Onto a Line [Passing Linear Algebra]

[@MissSixlane]

So helpful! Thank you so much!

[@kamogelomorole256]

Good explanation 👊🏾

[@omarshoukry4402]

Very helpful!!! Thank you

[@jamiedeal8160]

I'm confused how to apply this when the span of W is more than one vector

[@crystalfruit1193]

I think if you use gram-schmidt thats how you solve it. Not sure though

[@jhonsonholland5093]

I was wondering if the second method would work for a subspace more than 1dimension. How would we use the second method if the subspace was 2 dimension in R^3???

[@Anthony_Delcoro]

It does, that is exactly what my homework assignment is asking about.

[@samirkhan6195]

Another simple method is by recognising the fact that orthogonal projection matrix will be symmetric matrix , let's call this P, and from spectral theorem - every symmetric matrix is orthogonally diagonalizable , and you already have all the required component of this orthogonal diagonalization , We know eigenvalues (1,0,0) , we know eigenvector corresponding to eigenvalue 1 , i.e. above given vector v_1 , Don't forget to normalize this, lets call normalized vector b_1, other eigen vectors are not required because we are gonna use Spectral decomposition and components corresponding to 0 eigenvalues will be anyway 0 ...
A = 1(b_1 b_1^T) --- That's it.

[@ronak859]

Does this work in R2 for projecting onto a line

[@stemsupport3645]

yes!

[@johntapp7980]

Thank you!

[@Stevez221]

Thanks!

[@aarons8711]

🖐🤚