Everything about Coordinate Vector totally explained
In
linear algebra, a
coordinate vector is an explicit representation of a vector in an
abstract vector space as an ordered list of numbers or, equivalently, as an element of the
coordinate space Fn.Coordinate vectors allow calculations with
abstract objects to be transformed into calculations with blocks of numbers (
matrices and
column vectors), which we know how to do explicitly.
Definition
Let
V be a
vector space of
dimension n over a
field F and let
»
notice that the M's sub-index and v's sub-index are "canceling" each other and the M's sub-index is what remains and become v's new sub-index. The "canceling" of index isn't a real canceling but rather a manipulation of symbols which serves us for purposes of convenience.
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