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@jemoka / Jemoka Knowledge Base / wiki/concepts/linear_combination.md
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--- title: "linear combination" type: concept related: [Vector, Linear Combination] source: https://www.jemoka.com/posts/kbhlinear_combination/ confidence: high status: active --- A Linear Combination of vectors is a… guess what? Any vector formed by a combination of vectors at arbitrary scales. constituents A list of vectors \(v_1, \dots,v_{m}\) Scalars \(a_1, \dots, v_{m} \in \mathbb{F}\) requirements A Linear Combination is defined formally by: \begin{equation} v = a_1v_1+\dots+a_{m}v_{m} \end{equation}