According to Wikipedia:
"In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars."
Is this accurate? I mean, can we say that "linear functional", "covector" and "one-form" are synonyms?
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$\begingroup$Yes, you can say they are synonyms, just as the words function, map, and transformation all generally refer to the same thing. Sometimes it's just a matter of context whether one synonym will be preferred over the other, for example, as G. Sassatelli mentions. In my experience, "one-form" will be used generally when you are talking about exterior algebra things, for example when dealing with differential forms on a manifold. I'm not too sure about the difference in usages between the other two, however.
$\endgroup$ $\begingroup$I would say that the terms are completely equivalent in the linear algebra context. As just pointed out in the previous answer, the terms can have a more specific meaning in different contexts. For example when one talks about 'one-form'on a manifold, the 'one-form' is actually a map that assign to each point of the manifold a covector on the tangent space (i.e. a linear map on the tangent space), in other words it is a collection of linear maps on different vector spaces.
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