howa can i project M-1 vectors to it's orthogonal subspace ⟨A1⟩⊥ (A1 is a vector ) in matlab

howa can i project M-1 vectors to it's orthogonal subspace ⟨A1⟩⊥ (A1 is a vector ) in matlab;

and Find the band A2 with the maximum projection in ⟨A1⟩⊥, which is considered as the most dissimilar to A1.

Answer 1

[John D'Errico]

Huh? The projection of any of a set of vectors into a subspace that is orthogonal to that set will be the zero vector.

So you seem confused about what you are asking. If all you want is to find the nullspace of a set of vectors, then it is trivial. This is not a projection though.

help null

Or maybe you are asking to compute an orthogonal basis for A1.

help orth

As for asking to "Find the band A2 with the maximum projection in ⟨A1⟩⊥, which is considered as the most dissimilar to A1." this has zero meaning. Sorry.

The most dissimilar to the subspace spanned by A1 will arguably be the nullspace of A1. That will have zero projection on the vectors in A1.

[BANI tita]

sorry , My ask is: I have an original M-band(vectors) data set, and i want to do :

1) Randomly select a band A1, and project all the other M − 1 bands to its orthogonal subspace ⟨A1⟩⊥.

2) Find the band A2 with the maximum projection in ⟨A1⟩⊥, which is considered as the most dissimilar to A1.

thanks for your help