A git repository is a content-addressable object store where objects go in indexed by the SHA1 of their content, plus a set of named references pointing at specific objects by hash. The on-disk format (loose objects as individual files, packfiles as delta-compressed archives with a separate index, a ref store split between a directory of files and a packed-refs flat file with a locking protocol that breaks on NFS) is an implementation detail. The protocol for synchronising objects and refs between repositories is what actually matters, and since git-the-program is just one implementation of it, you can swap the storage backend without clients noticing.
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Another way to approach the linear combination is to look at it geometrically. This is where the idea of barycentric coordinates can help. A barycentric coordinate system describes the location of a point as the weighted sum of the regular coordinates of the vertices forming a simplex. In other words, it describes a linear combination with respect to a set of points, where in -dimensional space.
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