Definition:Generator of Vector Space/Also known as

Generator of Vector Space: Also known as

A generator of a vector space is also known as a spanning set.

Thus such a generator is said to span that vector space.

Some sources refer to a generator for rather than generator of. The two terms mean the same.

It can also be said that $S$ generates $\mathbf V$ (over $K$).

Other terms for $S$ are:

• A generating set of $\mathbf V$ (over $K$)
• A generating system of $\mathbf V$ (over $K$)

Some sources refer to such an $S$ as a set of generators of $\mathbf V$ over $K$ but this terminology is misleading, as it can be interpreted to mean that each of the elements of $S$ is itself a generator of $\mathbf V$ independently of the other elements.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): span
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): vector space (linear space)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): span
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): vector space (linear space)