is , and the previous expression for reduces to the empty sum. The standard convention for the empty sum implies thus a property that is immediate with the other definitions. However, many introductory textbooks simply include this fact as part of the definition.

When is finite, one has

Examples

The real vector space has {(-1, 0, 0), (0, 1, 0), (0, 0, 1)} as a spanning set. This particular spanning set is

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