Question

What is F^n in vector space..?? i mean its difference with R^n.. in the same context?

Answer 1

n tuples over a field F which might not be the real numbers \(\mathbb{R}\)

Answer 2

so it is somewhat more general, as F could be R but it could be something else

Answer 3

like what .. could you please elaborate with an example..

Answer 4

do you know any fields besides the field of real numbers?

Answer 5

one example would be \(\mathbb{Q}\) the field of rational numbers
or \(\mathbb{C}\) the field of complex numbers

Answer 6

but there are others, quaternions for example, or \(\mathbb{Z}_p\) for a prime \(p\)

Answer 7

in our class today our teacher dealt with coordination vector.. is there really something like that or is it a self coinage?

Answer 8

means \(<a_1, a_2, a_3,...,a_n>\) where \(a_i\in F\)

Answer 9

for whatever field F you are considering. it could be real numbers, or complex numbers or whatever

Answer 10

so \[a_{i}\] may be complex ...?then it gets difficult to visualize the concept. Does co-ordination vector has any graphical significance(in terms of linear dependency)