- #1

- 133

- 3

## Summary:

- Trying to get the basics of Covectors into my head.

## Main Question or Discussion Point

I understand that the Dual Space is composed of elements that linearly map the elements of the Vector Space onto Real numbers

If my preamble shows that I have understood correctly the basic premise, I have one or two questions that I am trying to work through.

So:

1: Is there a one to one correspondence between the elements of V and V* ? (Do the two sets have the same cardinality?)

2: Are the linear mappings that occur in V* all dot product relationships or are there different linear maps that accomplish the same end?

3: What actually distinguishes V from V* ? They are not identical sets are they?

If my preamble shows that I have understood correctly the basic premise, I have one or two questions that I am trying to work through.

So:

1: Is there a one to one correspondence between the elements of V and V* ? (Do the two sets have the same cardinality?)

2: Are the linear mappings that occur in V* all dot product relationships or are there different linear maps that accomplish the same end?

3: What actually distinguishes V from V* ? They are not identical sets are they?