Mixing
Should I use pseudo-inverses to prove this?
0
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Let $A=A(x)$ be a square matrix and let $x^*$ be such that $A(x^* )z=0$ and $z≥0$. Let $A(x)y≫0$ for $x≠x^*$. Then $z≯0$.
How to prove this? Should I use pseudo-inverses?
matrices pseudoinverse
asked Jan 10 at 16:41
a.giannela.giannel
163
$endgroup$
add a comment |
0
$begingroup$
Let $A=A(x)$ be a square matrix and let $x^*$ be such that $A(x^* )z=0$ and $z≥0$. Let $A(x)y≫0$ for $x≠x^*$. Then $z≯0$.
How to prove this? Should I use pseudo-inverses?
matrices pseudoinverse
asked Jan 10 at 16:41
a.giannela.giannel
163
$endgroup$
$begingroup$
Your question is hard to understand. It lacks appropriate quantifiers ("for all", "for some" etc.). It is not clear whether you are talking about some particular $x,y,z$ or not. And what is $y$? What does the symbol ≫ mean? Is $A$ entrywise positive or entrywise nonnegative?
$endgroup$
– user1551
Jan 11 at 11:53
$begingroup$
Thank you for your comment.Let $A=A(x)$ be a square matrix and let $x∗$ be such that $A(x∗)z=0$ for some $z≥0$. Let $A(x)y≫0$ for $x≠x∗$. Then $z≯0$. the symbol $≫$ means "much bigger than". It is there to prevent $A(x)y$ tending to zero as $x$ tends to $x∗$. For $A$, I am working with an M-matrix, but I thought this could work for any matrix, at least real matrix. Not sure though.
$endgroup$
– a.giannel
Jan 12 at 14:29
add a comment |
0
0
0
$begingroup$
Let $A=A(x)$ be a square matrix and let $x^*$ be such that $A(x^* )z=0$ and $z≥0$. Let $A(x)y≫0$ for $x≠x^*$. Then $z≯0$.
How to prove this? Should I use pseudo-inverses?
matrices pseudoinverse
asked Jan 10 at 16:41
a.giannela.giannel
163
$endgroup$
Let $A=A(x)$ be a square matrix and let $x^*$ be such that $A(x^* )z=0$ and $z≥0$. Let $A(x)y≫0$ for $x≠x^*$. Then $z≯0$.
How to prove this? Should I use pseudo-inverses?
matrices pseudoinverse
matrices pseudoinverse
asked Jan 10 at 16:41
a.giannela.giannel
163
asked Jan 10 at 16:41
a.giannela.giannel
163
asked Jan 10 at 16:41
a.giannela.giannel
163
asked Jan 10 at 16:41
a.giannela.giannel
163
asked Jan 10 at 16:41
a.giannela.giannel
163
163
$begingroup$
Your question is hard to understand. It lacks appropriate quantifiers ("for all", "for some" etc.). It is not clear whether you are talking about some particular $x,y,z$ or not. And what is $y$? What does the symbol ≫ mean? Is $A$ entrywise positive or entrywise nonnegative?
$endgroup$
– user1551
Jan 11 at 11:53
$begingroup$
Thank you for your comment.Let $A=A(x)$ be a square matrix and let $x∗$ be such that $A(x∗)z=0$ for some $z≥0$. Let $A(x)y≫0$ for $x≠x∗$. Then $z≯0$. the symbol $≫$ means "much bigger than". It is there to prevent $A(x)y$ tending to zero as $x$ tends to $x∗$. For $A$, I am working with an M-matrix, but I thought this could work for any matrix, at least real matrix. Not sure though.
$endgroup$
– a.giannel
Jan 12 at 14:29
add a comment |
$begingroup$
Your question is hard to understand. It lacks appropriate quantifiers ("for all", "for some" etc.). It is not clear whether you are talking about some particular $x,y,z$ or not. And what is $y$? What does the symbol ≫ mean? Is $A$ entrywise positive or entrywise nonnegative?
$endgroup$
– user1551
Jan 11 at 11:53
$begingroup$
Thank you for your comment.Let $A=A(x)$ be a square matrix and let $x∗$ be such that $A(x∗)z=0$ for some $z≥0$. Let $A(x)y≫0$ for $x≠x∗$. Then $z≯0$. the symbol $≫$ means "much bigger than". It is there to prevent $A(x)y$ tending to zero as $x$ tends to $x∗$. For $A$, I am working with an M-matrix, but I thought this could work for any matrix, at least real matrix. Not sure though.
$endgroup$
– a.giannel
Jan 12 at 14:29
$begingroup$
Your question is hard to understand. It lacks appropriate quantifiers ("for all", "for some" etc.). It is not clear whether you are talking about some particular $x,y,z$ or not. And what is $y$? What does the symbol ≫ mean? Is $A$ entrywise positive or entrywise nonnegative?
$endgroup$
– user1551
Jan 11 at 11:53
$begingroup$
Your question is hard to understand. It lacks appropriate quantifiers ("for all", "for some" etc.). It is not clear whether you are talking about some particular $x,y,z$ or not. And what is $y$? What does the symbol ≫ mean? Is $A$ entrywise positive or entrywise nonnegative?
$endgroup$
– user1551
Jan 11 at 11:53
$begingroup$
Thank you for your comment.Let $A=A(x)$ be a square matrix and let $x∗$ be such that $A(x∗)z=0$ for some $z≥0$. Let $A(x)y≫0$ for $x≠x∗$. Then $z≯0$. the symbol $≫$ means "much bigger than". It is there to prevent $A(x)y$ tending to zero as $x$ tends to $x∗$. For $A$, I am working with an M-matrix, but I thought this could work for any matrix, at least real matrix. Not sure though.
$endgroup$
– a.giannel
Jan 12 at 14:29
$begingroup$
Thank you for your comment.Let $A=A(x)$ be a square matrix and let $x∗$ be such that $A(x∗)z=0$ for some $z≥0$. Let $A(x)y≫0$ for $x≠x∗$. Then $z≯0$. the symbol $≫$ means "much bigger than". It is there to prevent $A(x)y$ tending to zero as $x$ tends to $x∗$. For $A$, I am working with an M-matrix, but I thought this could work for any matrix, at least real matrix. Not sure though.
$endgroup$
– a.giannel
Jan 12 at 14:29
add a comment |
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$begingroup$
Your question is hard to understand. It lacks appropriate quantifiers ("for all", "for some" etc.). It is not clear whether you are talking about some particular $x,y,z$ or not. And what is $y$? What does the symbol ≫ mean? Is $A$ entrywise positive or entrywise nonnegative?
$endgroup$
– user1551
Jan 11 at 11:53
$begingroup$
Thank you for your comment.Let $A=A(x)$ be a square matrix and let $x∗$ be such that $A(x∗)z=0$ for some $z≥0$. Let $A(x)y≫0$ for $x≠x∗$. Then $z≯0$. the symbol $≫$ means "much bigger than". It is there to prevent $A(x)y$ tending to zero as $x$ tends to $x∗$. For $A$, I am working with an M-matrix, but I thought this could work for any matrix, at least real matrix. Not sure though.
$endgroup$
– a.giannel
Jan 12 at 14:29