Dimension of Subspaces

Question

0

Consider two subspaces V and W of $\mathbb{R}^n$. Show that dim(V) + dim(W) = dim(V ∩ W) + dim(V + W).

Can anyone provide me with the proof for this?

asked 2017-02-14

user id:353506

83

1

Can? Yes. Will? No. – 2017-02-14
2

Think of a map from $V \times W \to \mathbb{R}^n$, whose kernel is $V \cap W$ and image is $V+W$. – 2017-02-14

0 Answers 0

Think of a map from $V \times W \to \mathbb{R}^n$, whose kernel is $V \cap W$ and image is $V+W$. — 2017-02-14