Let S now specifically be a one-dimensional subspace of V such that, for all →v∈V,
S={a→v:a∈F}
I think such S can not exist in most cases, and it should instead read ‘… for some →v∈V…’
The expression for S is describing the span of the vector →v, so certainly if V is more than one-dimensional, if some subspace S has this property for all→v∈V then it has this property for linearly independent vectors in V, which is a contradiction.
I think such S can not exist in most cases, and it should instead read ‘… for some →v∈V…’
The expression for S is describing the span of the vector →v, so certainly if V is more than one-dimensional, if some subspace S has this property for all →v∈V then it has this property for linearly independent vectors in V, which is a contradiction.