Duality and Inner Products

Date: 07 February 2018

Dual space

Duality in Euclidean spaces

In fact, the linear transformations $\lambda_w$ are all the linear transformations, i.e., the map $ev: V \to V^*$ is bijective, as we see from the following theorem.

Theorem: Let $\alpha: V \to \mathbb{R}$ be any linear functional. Then there exists a vector $w \in V$ such that $\alpha = \lambda_w$, i.e., for all $v\in V$, $\alpha(v) = \lambda_w(v)$.


All notes