I know that the standard basis for polynomials of degree n is
{${1,x,x^2,...,x^n}$}
but why is the 1 in there? After all, can't 1 be written as a linear combination, where
$c_1 = 1/x$
and
$1 = x*c_1 $
I know that the standard basis for polynomials of degree n is
{${1,x,x^2,...,x^n}$}
but why is the 1 in there? After all, can't 1 be written as a linear combination, where
$c_1 = 1/x$
and
$1 = x*c_1 $
$c_1=1/x$ is neither a scalar nor a polynomial.
You have confused the notion of a basis, see here: