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Alle videoervector spaces

Subspaces: Why the Origin Matters

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A subspace must contain the zero vector, be closed under addition, and be closed under scalar multiplication. A line through the origin passes all three tests. A line that misses the origin fails closure under addition — the parallelogram-rule sum of two of its vectors lands off the line, and the origin is not on the line either.

subspaceclosure under additionclosure under scalar multiplicationzero vectoraffine setvector space
ForutsetterSpan and Linear Dependence