KBxDirectSum

Don't have the same rules when you add two together and many together! Intersection of zero != direct sum when you are adding more than one.

$ u₁ + u₂ + … + u_n = {u₁+u₂ + … + u_n \mid u₁ ∈ U₁ , … , u_n ∈ U_n} $

If the direct sum requirements are not true, then it's just a sum.

Direct sum is all possible combos?

When all the vectors inside the direct sum are linearly dependent, then you can't make a direct sum with them? Because really, \(u_1 \in u_2\) Because the sums will not be unique. Redundancy!

$ U₁ = {

\begin{bmatrix} 1 \\ 0 \end{bmatrix}

} $ $ U₂ = {

\begin{bmatrix} 2 \\ 0 \end{bmatrix}

} $ doesn't work, cus you can just multiply all in \(U_1\) by 2 to get things in \(U_2\)