Mixing
Terminology question in linear algebra - a set that is closed under multiplication.
$begingroup$
Let $X$ be a (real) vector space.
Let $S$ be a nonempty subset of $X$.
If $S$ is closed under addition and scalar multiplication,
then we call $S$ a subspace.
If $S$ is closed under multiplication by nonnegative scalars,
then we call $S$ a cone (that may or may not be convex).
My question is:
What do we call $S$ if $S$ is closed under scalar multiplication?
Note: $S$ need not be closed under addition.
linear-algebra vector-spaces terminology
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
$endgroup$
add a comment |
$begingroup$
Let $X$ be a (real) vector space.
Let $S$ be a nonempty subset of $X$.
If $S$ is closed under addition and scalar multiplication,
then we call $S$ a subspace.
If $S$ is closed under multiplication by nonnegative scalars,
then we call $S$ a cone (that may or may not be convex).
My question is:
What do we call $S$ if $S$ is closed under scalar multiplication?
Note: $S$ need not be closed under addition.
linear-algebra vector-spaces terminology
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
$endgroup$
add a comment |
$begingroup$
Let $X$ be a (real) vector space.
Let $S$ be a nonempty subset of $X$.
If $S$ is closed under addition and scalar multiplication,
then we call $S$ a subspace.
If $S$ is closed under multiplication by nonnegative scalars,
then we call $S$ a cone (that may or may not be convex).
My question is:
What do we call $S$ if $S$ is closed under scalar multiplication?
Note: $S$ need not be closed under addition.
linear-algebra vector-spaces terminology
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
$endgroup$
Let $X$ be a (real) vector space.
Let $S$ be a nonempty subset of $X$.
If $S$ is closed under addition and scalar multiplication,
then we call $S$ a subspace.
If $S$ is closed under multiplication by nonnegative scalars,
then we call $S$ a cone (that may or may not be convex).
My question is:
What do we call $S$ if $S$ is closed under scalar multiplication?
Note: $S$ need not be closed under addition.
linear-algebra vector-spaces terminology
linear-algebra vector-spaces terminology
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
asked Feb 1 at 18:55
max_zornmax_zorn
3,44061429
3,44061429
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Following Bourbaki (EVT I.1.5 Definition 3, II.2.4 Definition 3), such a thing may be called a balanced cone.
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
$endgroup$
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
add a comment |
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Following Bourbaki (EVT I.1.5 Definition 3, II.2.4 Definition 3), such a thing may be called a balanced cone.
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
$endgroup$
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
add a comment |
$begingroup$
Following Bourbaki (EVT I.1.5 Definition 3, II.2.4 Definition 3), such a thing may be called a balanced cone.
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
$endgroup$
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
add a comment |
$begingroup$
Following Bourbaki (EVT I.1.5 Definition 3, II.2.4 Definition 3), such a thing may be called a balanced cone.
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
$endgroup$
Following Bourbaki (EVT I.1.5 Definition 3, II.2.4 Definition 3), such a thing may be called a balanced cone.
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
answered Feb 1 at 19:34
Fred RohrerFred Rohrer
386110
386110
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
add a comment |
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
$begingroup$
Fantastic, exactly what I was looking for. Thanks very much!
$endgroup$
– max_zorn
Feb 2 at 20:15
add a comment |
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