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Suppose $T: \mathbb{R}^2 \to \mathbb{R}^2$ is defined as $$T(x,y) = \begin{bmatrix}2x-y \\ x+3y \end{bmatrix}$$

Find the adjoint $T^{*}$ of $T$. So we can create a linear functional as follows: Choose $w = (x,y)$. Then $$T_{w}(x,y) = \langle(2x-y,x+3y), (x,y) \rangle$$

So then we need to find the vector $T^{*}w$ such that $$\langle Tv, w \rangle = \langle v, T^{*}w \rangle$$ for all $w \in W$ and $v \in V$.

  • 0
    We need to? What have you done so far? Where are you stuck? What is your question?2012-07-18
  • 1
    $T$ is represented by the matrix \begin{bmatrix} 2 & -1 \\ 1 & 3 \end{bmatrix}2012-07-18

1 Answers 1