Coordinate functional ( $e_{i}^{*} (\sum_{j} a_{j} e_{j}) = a_{i}$ )

A coordinate functional extracts one coefficient in a specified finite basis. It is an element of that basis's dual basis, rather than a coordinate rule independent of the basis. For the standard basis of

F^{n}

, the

i

th coordinate functional sends

(a_{1}, \dots, a_{n})

to

a_{i}

.

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