Is arbitrary direct sum of vector spaces vector space?
0
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Suddenly thinking about arbitrary direct sum of the real numbers R, I came across this question. Can someone answer this?
linear-algebra
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
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add a comment |
0
$begingroup$
Suddenly thinking about arbitrary direct sum of the real numbers R, I came across this question. Can someone answer this?
linear-algebra
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
$endgroup$
1
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The answer is yes.
$endgroup$
– Hanul Jeon
Dec 26 '18 at 9:46
1
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Yes, it is... if the factors are vector spaces over the same field . Whether you're thinking of internal direct sum (of subspaces of some space) or external one with the obvious definition, it is always a linear space
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– DonAntonio
Dec 26 '18 at 9:47
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Welcome to MSE. The title of a question should not be its first sentence.
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– José Carlos Santos
Dec 26 '18 at 9:55
add a comment |
0
0
0
$begingroup$
Suddenly thinking about arbitrary direct sum of the real numbers R, I came across this question. Can someone answer this?
linear-algebra
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
$endgroup$
Suddenly thinking about arbitrary direct sum of the real numbers R, I came across this question. Can someone answer this?
linear-algebra
linear-algebra
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
asked Dec 26 '18 at 9:40
Debayan GoswamiDebayan Goswami
11
11
1
$begingroup$
The answer is yes.
$endgroup$
– Hanul Jeon
Dec 26 '18 at 9:46
1
$begingroup$
Yes, it is... if the factors are vector spaces over the same field . Whether you're thinking of internal direct sum (of subspaces of some space) or external one with the obvious definition, it is always a linear space
$endgroup$
– DonAntonio
Dec 26 '18 at 9:47
$begingroup$
Welcome to MSE. The title of a question should not be its first sentence.
$endgroup$
– José Carlos Santos
Dec 26 '18 at 9:55
add a comment |
1
$begingroup$
The answer is yes.
$endgroup$
– Hanul Jeon
Dec 26 '18 at 9:46
1
$begingroup$
Yes, it is... if the factors are vector spaces over the same field . Whether you're thinking of internal direct sum (of subspaces of some space) or external one with the obvious definition, it is always a linear space
$endgroup$
– DonAntonio
Dec 26 '18 at 9:47
$begingroup$
Welcome to MSE. The title of a question should not be its first sentence.
$endgroup$
– José Carlos Santos
Dec 26 '18 at 9:55
1
1
$begingroup$
The answer is yes.
$endgroup$
– Hanul Jeon
Dec 26 '18 at 9:46
$begingroup$
The answer is yes.
$endgroup$
– Hanul Jeon
Dec 26 '18 at 9:46
1
1
$begingroup$
Yes, it is... if the factors are vector spaces over the same field . Whether you're thinking of internal direct sum (of subspaces of some space) or external one with the obvious definition, it is always a linear space
$endgroup$
– DonAntonio
Dec 26 '18 at 9:47
$begingroup$
Yes, it is... if the factors are vector spaces over the same field . Whether you're thinking of internal direct sum (of subspaces of some space) or external one with the obvious definition, it is always a linear space
$endgroup$
– DonAntonio
Dec 26 '18 at 9:47
$begingroup$
Welcome to MSE. The title of a question should not be its first sentence.
$endgroup$
– José Carlos Santos
Dec 26 '18 at 9:55
$begingroup$
Welcome to MSE. The title of a question should not be its first sentence.
$endgroup$
– José Carlos Santos
Dec 26 '18 at 9:55
add a comment |
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1
$begingroup$
The answer is yes.
$endgroup$
– Hanul Jeon
Dec 26 '18 at 9:46
1
$begingroup$
Yes, it is... if the factors are vector spaces over the same field . Whether you're thinking of internal direct sum (of subspaces of some space) or external one with the obvious definition, it is always a linear space
$endgroup$
– DonAntonio
Dec 26 '18 at 9:47
$begingroup$
Welcome to MSE. The title of a question should not be its first sentence.
$endgroup$
– José Carlos Santos
Dec 26 '18 at 9:55