Question

how to prove that two subspace are orthagonal

Answer 1

if you can show that no matter what vector you choose from the subspaces, that their inner product is 0, then those spaces are orthogonal.

Answer 2

Basically, if V and W are subspaces:\[\forall v\in V, \forall w\in W, \langle v,w\rangle=0\]

Answer 3

imran you wanna medal

Answer 4

how do we prove that any vector in subspace is orthagonal to vector in other subspace

Answer 5

This usually boils down showing that the basis vectors of the space v are orthogonal to the basis vectors of the space W. Because then any vector is just a linear combination of the basis vectors, and the inner product will always evaluate to 0.

Answer 6

thanks

Answer 7

welcome :) go linear algebra!