Subspaces of a complex vector space
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The exercise is to prove that the set of complex numbers is a linear space over the field of complex numbers and to find two subspaces (not the trivial and the space itself). I was able to show the first part but i'm not able to find two subspaces (if there's any). I'd like a hint on how to approach the second part.
linear-algebra
asked Nov 13 at 21:46
mxaxc
976
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up vote
0
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The exercise is to prove that the set of complex numbers is a linear space over the field of complex numbers and to find two subspaces (not the trivial and the space itself). I was able to show the first part but i'm not able to find two subspaces (if there's any). I'd like a hint on how to approach the second part.
linear-algebra
asked Nov 13 at 21:46
mxaxc
976
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The exercise is to prove that the set of complex numbers is a linear space over the field of complex numbers and to find two subspaces (not the trivial and the space itself). I was able to show the first part but i'm not able to find two subspaces (if there's any). I'd like a hint on how to approach the second part.
linear-algebra
asked Nov 13 at 21:46
mxaxc
976
The exercise is to prove that the set of complex numbers is a linear space over the field of complex numbers and to find two subspaces (not the trivial and the space itself). I was able to show the first part but i'm not able to find two subspaces (if there's any). I'd like a hint on how to approach the second part.
linear-algebra
linear-algebra
asked Nov 13 at 21:46
mxaxc
976
asked Nov 13 at 21:46
mxaxc
976
asked Nov 13 at 21:46
mxaxc
976
asked Nov 13 at 21:46
mxaxc
976
asked Nov 13 at 21:46
mxaxc
976
976
add a comment |
add a comment |
1 Answer
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There are no other subspaces of $mathbb C$. This is because $dim_mathbb C(mathbb C)=1$, so any subspace of $mathbb C$ has either dimension $1$ or $0$. The latter case is the zero space, and the former case is the entire space $mathbb C$.
answered Nov 13 at 21:54
Dave
8,40811033
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
There are no other subspaces of $mathbb C$. This is because $dim_mathbb C(mathbb C)=1$, so any subspace of $mathbb C$ has either dimension $1$ or $0$. The latter case is the zero space, and the former case is the entire space $mathbb C$.
answered Nov 13 at 21:54
Dave
8,40811033
add a comment |
up vote
4
down vote
accepted
There are no other subspaces of $mathbb C$. This is because $dim_mathbb C(mathbb C)=1$, so any subspace of $mathbb C$ has either dimension $1$ or $0$. The latter case is the zero space, and the former case is the entire space $mathbb C$.
answered Nov 13 at 21:54
Dave
8,40811033
add a comment |
up vote
4
down vote
accepted
up vote
4
down vote
accepted
There are no other subspaces of $mathbb C$. This is because $dim_mathbb C(mathbb C)=1$, so any subspace of $mathbb C$ has either dimension $1$ or $0$. The latter case is the zero space, and the former case is the entire space $mathbb C$.
answered Nov 13 at 21:54
Dave
8,40811033
There are no other subspaces of $mathbb C$. This is because $dim_mathbb C(mathbb C)=1$, so any subspace of $mathbb C$ has either dimension $1$ or $0$. The latter case is the zero space, and the former case is the entire space $mathbb C$.
answered Nov 13 at 21:54
Dave
8,40811033
answered Nov 13 at 21:54
Dave
8,40811033
answered Nov 13 at 21:54
Dave
8,40811033
answered Nov 13 at 21:54
Dave
8,40811033
8,40811033
add a comment |
add a comment |
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