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 21 hours ago
Jimmy R.
32.8k42156
asked yesterday
Bn.F76
85
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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 21 hours ago
Jimmy R.
32.8k42156
asked yesterday
Bn.F76
85
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
yesterday
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
yesterday
@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
yesterday
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
yesterday
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
yesterday
|
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 21 hours ago
Jimmy R.
32.8k42156
asked yesterday
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 21 hours ago
Jimmy R.
32.8k42156
asked yesterday
Bn.F76
85
edited 21 hours ago
Jimmy R.
32.8k42156
asked yesterday
Bn.F76
85
edited 21 hours ago
Jimmy R.
32.8k42156
edited 21 hours ago
Jimmy R.
32.8k42156
edited 21 hours ago
Jimmy R.
32.8k42156
32.8k42156
asked yesterday
Bn.F76
85
asked yesterday
Bn.F76
85
asked yesterday
Bn.F76
85
85
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
yesterday
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
yesterday
@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
yesterday
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
yesterday
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
yesterday
|
show 1 more comment
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
yesterday
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
yesterday
@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
yesterday
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
yesterday
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
yesterday
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
yesterday
Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
yesterday
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
yesterday
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
yesterday
@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
yesterday
@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
yesterday
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
yesterday
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
yesterday
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
yesterday
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
yesterday
|
show 1 more comment
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Is this tropical algebra? That certainly is not a vector space operation.
– Matt Samuel
yesterday
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
yesterday
@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
yesterday
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
yesterday
Got it. Thanks for the insight. The author is Gilbert Strang.
– Bn.F76
yesterday