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A general vector in $\mathbb{R}^4$ is decomposed by separating its coordinates into two blocks. The first two coordinates form a vector in $W$, and the last two coordinates form a vector in $W^\perp$.

Conditions: The ambient space is $\mathbb{R}^4$.; $W$ has basis $\left\{\begin{pmatrix}1\\0\\0\\0\end{pmatrix},\begin{pmatrix}0\\1\\0\\0\end{pmatrix}\right\}$.; $W^\perp$ has basis $\left\{\begin{pmatrix}0\\0\\1\\0\end{pmatrix},\begin{pmatrix}0\\0\\0\\1\end{pmatrix}\right\}$.; The vector is represented as $\begin{pmatrix}a\\b\\c\\d\end{pmatrix}$ with $a,b,c,d \in \mathbb{R}$.

A general vector in $\mathbb{R}^4$ is decomposed by separating its coordinates into two blocks. The first two coordinates form a vector in $W$, and the last two coordinates form a vector in $W^\perp$.

Conditions: The ambient space is $\mathbb{R}^4$.; $W$ has basis $\left\{\begin{pmatrix}1\\0\\0\\0\end{pmatrix},\begin{pmatrix}0\\1\\0\\0\end{pmatrix}\right\}$.; $W^\perp$ has basis $\left\{\begin{pmatrix}0\\0\\1\\0\end{pmatrix},\begin{pmatrix}0\\0\\0\\1\end{pmatrix}\right\}$.; The vector is represented as $\begin{pmatrix}a\\b\\c\\d\end{pmatrix}$ with $a,b,c,d \in \mathbb{R}$.