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







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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















up vote
1
down vote

favorite
1












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







share|cite|improve this question
























  • 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













up vote
1
down vote

favorite
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up vote
1
down vote

favorite
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1





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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 19 hours ago









Jimmy R.

32.8k42156




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asked yesterday









Bn.F76

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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


















  • 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















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