Which $y$ is the zero vector that gives $x + mathbf0 = max{(x, mathbf0)}= x$ for every $x$?
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This was a note in my Linear Algebra textbook after the column space chapter. I'm so confused. Is the answer: "$y$ is the $n$ dimensional column vector where each element is negative infinity." ?
Note : An interesting “max-plus” vector space comes from the real numbers $mathbf R$ combined with $-infty$. Change addition to give $x + y = max{(x, y)}$ and change multiplication to $xy =$ usual $x + y$. Which $y$ is the zero vector that gives $x + 0 = max{(x, 0)} = x$ for every $x$?
edit: here is a picture
linear-algebra abstract-algebra
edited Nov 19 at 10:25
Jimmy R.
33k42157
asked Nov 19 at 2:14
Bn.F76
85
|
show 1 more comment
up vote
1
down vote
favorite
This was a note in my Linear Algebra textbook after the column space chapter. I'm so confused. Is the answer: "$y$ is the $n$ dimensional column vector where each element is negative infinity." ?
Note : An interesting “max-plus” vector space comes from the real numbers $mathbf R$ combined with $-infty$. Change addition to give $x + y = max{(x, y)}$ and change multiplication to $xy =$ usual $x + y$. Which $y$ is the zero vector that gives $x + 0 = max{(x, 0)} = x$ for every $x$?
edit: here is a picture
linear-algebra abstract-algebra
edited Nov 19 at 10:25
Jimmy R.
33k42157
asked Nov 19 at 2:14
Bn.F76
85
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
Nov 19 at 2:37
The answer is $-infty$, except the question is ill posed because it's just not a vector space. Is this translated from another language?
– Matt Samuel
Nov 19 at 2:40
@MattSamuel Okay thanks. No it's not translated, literally a note in the answer key. I'm studying normal linear algebra so it's definitely not tropical algebra.
– Bn.F76
Nov 19 at 2:42
Well that's basically the definition of a tropical ring. Maybe the author was studying tropical algebra while writing this and hastily added this confused note.
– Matt Samuel
Nov 19 at 2:44
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
Nov 19 at 2:45
|
show 1 more comment
up vote
1
down vote
favorite
up vote
1
down vote
favorite
This was a note in my Linear Algebra textbook after the column space chapter. I'm so confused. Is the answer: "$y$ is the $n$ dimensional column vector where each element is negative infinity." ?
Note : An interesting “max-plus” vector space comes from the real numbers $mathbf R$ combined with $-infty$. Change addition to give $x + y = max{(x, y)}$ and change multiplication to $xy =$ usual $x + y$. Which $y$ is the zero vector that gives $x + 0 = max{(x, 0)} = x$ for every $x$?
edit: here is a picture
linear-algebra abstract-algebra
edited Nov 19 at 10:25
Jimmy R.
33k42157
asked Nov 19 at 2:14
Bn.F76
85
This was a note in my Linear Algebra textbook after the column space chapter. I'm so confused. Is the answer: "$y$ is the $n$ dimensional column vector where each element is negative infinity." ?
Note : An interesting “max-plus” vector space comes from the real numbers $mathbf R$ combined with $-infty$. Change addition to give $x + y = max{(x, y)}$ and change multiplication to $xy =$ usual $x + y$. Which $y$ is the zero vector that gives $x + 0 = max{(x, 0)} = x$ for every $x$?
edit: here is a picture
linear-algebra abstract-algebra
linear-algebra abstract-algebra
edited Nov 19 at 10:25
Jimmy R.
33k42157
asked Nov 19 at 2:14
Bn.F76
85
edited Nov 19 at 10:25
Jimmy R.
33k42157
asked Nov 19 at 2:14
Bn.F76
85
edited Nov 19 at 10:25
Jimmy R.
33k42157
edited Nov 19 at 10:25
Jimmy R.
33k42157
edited Nov 19 at 10:25
Jimmy R.
33k42157
33k42157
asked Nov 19 at 2:14
Bn.F76
85
asked Nov 19 at 2:14
Bn.F76
85
asked Nov 19 at 2:14
Bn.F76
85
85
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
Nov 19 at 2:37
The answer is $-infty$, except the question is ill posed because it's just not a vector space. Is this translated from another language?
– Matt Samuel
Nov 19 at 2:40
@MattSamuel Okay thanks. No it's not translated, literally a note in the answer key. I'm studying normal linear algebra so it's definitely not tropical algebra.
– Bn.F76
Nov 19 at 2:42
Well that's basically the definition of a tropical ring. Maybe the author was studying tropical algebra while writing this and hastily added this confused note.
– Matt Samuel
Nov 19 at 2:44
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
Nov 19 at 2:45
|
show 1 more comment
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
Nov 19 at 2:37
The answer is $-infty$, except the question is ill posed because it's just not a vector space. Is this translated from another language?
– Matt Samuel
Nov 19 at 2:40
@MattSamuel Okay thanks. No it's not translated, literally a note in the answer key. I'm studying normal linear algebra so it's definitely not tropical algebra.
– Bn.F76
Nov 19 at 2:42
Well that's basically the definition of a tropical ring. Maybe the author was studying tropical algebra while writing this and hastily added this confused note.
– Matt Samuel
Nov 19 at 2:44
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
Nov 19 at 2:45
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
Nov 19 at 2:37
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
Nov 19 at 2:37
The answer is $-infty$, except the question is ill posed because it's just not a vector space. Is this translated from another language?
– Matt Samuel
Nov 19 at 2:40
The answer is $-infty$, except the question is ill posed because it's just not a vector space. Is this translated from another language?
– Matt Samuel
Nov 19 at 2:40
@MattSamuel Okay thanks. No it's not translated, literally a note in the answer key. I'm studying normal linear algebra so it's definitely not tropical algebra.
– Bn.F76
Nov 19 at 2:42
@MattSamuel Okay thanks. No it's not translated, literally a note in the answer key. I'm studying normal linear algebra so it's definitely not tropical algebra.
– Bn.F76
Nov 19 at 2:42
Well that's basically the definition of a tropical ring. Maybe the author was studying tropical algebra while writing this and hastily added this confused note.
– Matt Samuel
Nov 19 at 2:44
Well that's basically the definition of a tropical ring. Maybe the author was studying tropical algebra while writing this and hastily added this confused note.
– Matt Samuel
Nov 19 at 2:44
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
Nov 19 at 2:45
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
Nov 19 at 2:45
|
show 1 more comment
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Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
Nov 19 at 2:37
The answer is $-infty$, except the question is ill posed because it's just not a vector space. Is this translated from another language?
– Matt Samuel
Nov 19 at 2:40
@MattSamuel Okay thanks. No it's not translated, literally a note in the answer key. I'm studying normal linear algebra so it's definitely not tropical algebra.
– Bn.F76
Nov 19 at 2:42
Well that's basically the definition of a tropical ring. Maybe the author was studying tropical algebra while writing this and hastily added this confused note.
– Matt Samuel
Nov 19 at 2:44
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
Nov 19 at 2:45