$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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A vector space $W$ is the direct sum of vector space $U$ and $V$ if $W=U+V$ and $U\cap V=0$. Alternatively, for every $w\in W$, there is a unique way of writing $w=u+v$, where $u\in U$, $v\in V$.
Alternative definition using independence: $W$ is the direct sum of $V_1, \dots, v_j$ if $W=V_1 + \dots, + V_k$ and $V_1, \dots, V_k$ are independent. The direct sum is denoted with $W=U\oplus V$

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A vector space $W$ is the direct sum of vector space $U$ and $V$ if $W=U+V$ and $U\cap V=0$. Alternatively, for every $w\in W$, there is a unique way of writing $w=u+v$, where $u\in U$, $v\in V$.
Alternative definition using independence: $W$ is the direct sum of $V_1, \dots, v_j$ if $W=V_1 + \dots, + V_k$ and $V_1, \dots, V_k$ are independent. The direct sum is denoted with $W=U\oplus V$

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definition
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FullPage
definition
concepts
used in
hypothesis
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A vector space $W$ is the direct sum of vector space $U$ and $V$ if $W=U+V$ and $U\cap V=0$. Alternatively, for every $w\in W$, there is a unique way of writing $w=u+v$, where $u\in U$, $v\in V$.
Alternative definition using independence: $W$ is the direct sum of $V_1, \dots, v_j$ if $W=V_1 + \dots, + V_k$ and $V_1, \dots, V_k$ are independent. The direct sum is denoted with $W=U\oplus V$

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A vector space $W$ is the direct sum of vector space $U$ and $V$ if $W=U+V$ and $U\cap V=0$. Alternatively, for every $w\in W$, there is a unique way of writing $w=u+v$, where $u\in U$, $v\in V$.
Alternative definition using independence: $W$ is the direct sum of $V_1, \dots, v_j$ if $W=V_1 + \dots, + V_k$ and $V_1, \dots, V_k$ are independent. The direct sum is denoted with $W=U\oplus V$

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